REF: Refactor Datetimelike delegation
This is a generalization of PeriodIndex's dispatching to
PeriodArray, without any actual changes yet. This is split
from #24024, where DatetimeIndex and TimedeltaIndex will
implement and inherit from delgates similiar to PeriodDelegateMixin.
Hello @TomAugspurger! Thanks for submitting the PR.

 - There are no PEP8 issues in the file [`pandas/core/indexes/datetimelike.py`](https://github.com/TomAugspurger/pandas/blob/e614a80668d630eb415bed25f861a49fa929d042/pandas/core/indexes/datetimelike.py) !

 - There are no PEP8 issues in the file [`pandas/core/indexes/period.py`](https://github.com/TomAugspurger/pandas/blob/e614a80668d630eb415bed25f861a49fa929d042/pandas/core/indexes/period.py) !

 These latest two commits have some actual changes:

1. Removes "delegation" for size, shape, and asi8. These were being overwritten anyway (I think).
2. Adds delegation for `asfreq` and `to_timestamp`. I don't understand my earlier comment about why they couldn't be dispatched normally (but perhaps tests will turn something up). # [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/24039?src=pr&el=h1) Report
> Merging [#24039](https://codecov.io/gh/pandas-dev/pandas/pull/24039?src=pr&el=desc) into [master](https://codecov.io/gh/pandas-dev/pandas/commit/5b0610b875476a6f3727d7e9bedb90d370c669b5?src=pr&el=desc) will **increase** coverage by `49.88%`.
> The diff coverage is `96.15%`.

[![Impacted file tree graph](https://codecov.io/gh/pandas-dev/pandas/pull/24039/graphs/tree.svg?width=650&token=eZ4WkYLtcO&height=150&src=pr)](https://codecov.io/gh/pandas-dev/pandas/pull/24039?src=pr&el=tree)

```diff
@@             Coverage Diff             @@
##           master   #24039       +/-   ##
===========================================
+ Coverage   42.46%   92.35%   +49.88%     
===========================================
  Files         161      161               
  Lines       51557    51562        +5     
===========================================
+ Hits        21892    47618    +25726     
+ Misses      29665     3944    -25721
```

| Flag | Coverage Δ | |
|---|---|---|
| #multiple | `90.75% <96.15%> (?)` | |
| #single | `42.47% <65.38%> (+0.01%)` | :arrow_up: |

| [Impacted Files](https://codecov.io/gh/pandas-dev/pandas/pull/24039?src=pr&el=tree) | Coverage Δ | |
|---|---|---|
| [pandas/core/indexes/period.py](https://codecov.io/gh/pandas-dev/pandas/pull/24039/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy9wZXJpb2QucHk=) | `93.06% <100%> (+53.23%)` | :arrow_up: |
| [pandas/core/indexes/datetimelike.py](https://codecov.io/gh/pandas-dev/pandas/pull/24039/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy9kYXRldGltZWxpa2UucHk=) | `97.59% <95%> (+45.05%)` | :arrow_up: |
| [pandas/core/computation/pytables.py](https://codecov.io/gh/pandas-dev/pandas/pull/24039/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvY29tcHV0YXRpb24vcHl0YWJsZXMucHk=) | `92.37% <0%> (+0.3%)` | :arrow_up: |
| [pandas/io/pytables.py](https://codecov.io/gh/pandas-dev/pandas/pull/24039/diff?src=pr&el=tree#diff-cGFuZGFzL2lvL3B5dGFibGVzLnB5) | `92.3% <0%> (+0.92%)` | :arrow_up: |
| [pandas/util/\_test\_decorators.py](https://codecov.io/gh/pandas-dev/pandas/pull/24039/diff?src=pr&el=tree#diff-cGFuZGFzL3V0aWwvX3Rlc3RfZGVjb3JhdG9ycy5weQ==) | `93.24% <0%> (+4.05%)` | :arrow_up: |
| [pandas/compat/\_\_init\_\_.py](https://codecov.io/gh/pandas-dev/pandas/pull/24039/diff?src=pr&el=tree#diff-cGFuZGFzL2NvbXBhdC9fX2luaXRfXy5weQ==) | `58.36% <0%> (+8.17%)` | :arrow_up: |
| [pandas/core/config\_init.py](https://codecov.io/gh/pandas-dev/pandas/pull/24039/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvY29uZmlnX2luaXQucHk=) | `99.24% <0%> (+9.84%)` | :arrow_up: |
| [pandas/core/reshape/util.py](https://codecov.io/gh/pandas-dev/pandas/pull/24039/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvcmVzaGFwZS91dGlsLnB5) | `100% <0%> (+11.53%)` | :arrow_up: |
| [pandas/compat/numpy/\_\_init\_\_.py](https://codecov.io/gh/pandas-dev/pandas/pull/24039/diff?src=pr&el=tree#diff-cGFuZGFzL2NvbXBhdC9udW1weS9fX2luaXRfXy5weQ==) | `92.85% <0%> (+14.28%)` | :arrow_up: |
| [pandas/core/computation/common.py](https://codecov.io/gh/pandas-dev/pandas/pull/24039/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvY29tcHV0YXRpb24vY29tbW9uLnB5) | `85.71% <0%> (+14.28%)` | :arrow_up: |
| ... and [121 more](https://codecov.io/gh/pandas-dev/pandas/pull/24039/diff?src=pr&el=tree-more) | |

------

[Continue to review full report at Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/24039?src=pr&el=continue).
> **Legend** - [Click here to learn more](https://docs.codecov.io/docs/codecov-delta)
> `Δ = absolute <relative> (impact)`, `ø = not affected`, `? = missing data`
> Powered by [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/24039?src=pr&el=footer). Last update [5b0610b...de13b2d](https://codecov.io/gh/pandas-dev/pandas/pull/24039?src=pr&el=lastupdated). Read the [comment docs](https://docs.codecov.io/docs/pull-request-comments).
 # [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/24039?src=pr&el=h1) Report
> Merging [#24039](https://codecov.io/gh/pandas-dev/pandas/pull/24039?src=pr&el=desc) into [master](https://codecov.io/gh/pandas-dev/pandas/commit/367efb280c69a55b676410bddc4497e744f90755?src=pr&el=desc) will **decrease** coverage by `49.85%`.
> The diff coverage is `67.85%`.

[![Impacted file tree graph](https://codecov.io/gh/pandas-dev/pandas/pull/24039/graphs/tree.svg?width=650&token=eZ4WkYLtcO&height=150&src=pr)](https://codecov.io/gh/pandas-dev/pandas/pull/24039?src=pr&el=tree)

```diff
@@             Coverage Diff             @@
##           master   #24039       +/-   ##
===========================================
- Coverage   92.31%   42.46%   -49.86%     
===========================================
  Files         161      161               
  Lines       51562    51568        +6     
===========================================
- Hits        47599    21896    -25703     
- Misses       3963    29672    +25709
```

| Flag | Coverage Δ | |
|---|---|---|
| #multiple | `?` | |
| #single | `42.46% <67.85%> (+0.01%)` | :arrow_up: |

| [Impacted Files](https://codecov.io/gh/pandas-dev/pandas/pull/24039?src=pr&el=tree) | Coverage Δ | |
|---|---|---|
| [pandas/core/indexes/period.py](https://codecov.io/gh/pandas-dev/pandas/pull/24039/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy9wZXJpb2QucHk=) | `40.84% <100%> (-52.23%)` | :arrow_down: |
| [pandas/core/indexes/datetimelike.py](https://codecov.io/gh/pandas-dev/pandas/pull/24039/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy9kYXRldGltZWxpa2UucHk=) | `53.63% <55%> (-43.79%)` | :arrow_down: |
| [pandas/io/formats/latex.py](https://codecov.io/gh/pandas-dev/pandas/pull/24039/diff?src=pr&el=tree#diff-cGFuZGFzL2lvL2Zvcm1hdHMvbGF0ZXgucHk=) | `0% <0%> (-100%)` | :arrow_down: |
| [pandas/core/categorical.py](https://codecov.io/gh/pandas-dev/pandas/pull/24039/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvY2F0ZWdvcmljYWwucHk=) | `0% <0%> (-100%)` | :arrow_down: |
| [pandas/io/sas/sas\_constants.py](https://codecov.io/gh/pandas-dev/pandas/pull/24039/diff?src=pr&el=tree#diff-cGFuZGFzL2lvL3Nhcy9zYXNfY29uc3RhbnRzLnB5) | `0% <0%> (-100%)` | :arrow_down: |
| [pandas/tseries/plotting.py](https://codecov.io/gh/pandas-dev/pandas/pull/24039/diff?src=pr&el=tree#diff-cGFuZGFzL3RzZXJpZXMvcGxvdHRpbmcucHk=) | `0% <0%> (-100%)` | :arrow_down: |
| [pandas/tseries/converter.py](https://codecov.io/gh/pandas-dev/pandas/pull/24039/diff?src=pr&el=tree#diff-cGFuZGFzL3RzZXJpZXMvY29udmVydGVyLnB5) | `0% <0%> (-100%)` | :arrow_down: |
| [pandas/io/formats/html.py](https://codecov.io/gh/pandas-dev/pandas/pull/24039/diff?src=pr&el=tree#diff-cGFuZGFzL2lvL2Zvcm1hdHMvaHRtbC5weQ==) | `0% <0%> (-97.98%)` | :arrow_down: |
| [pandas/core/groupby/categorical.py](https://codecov.io/gh/pandas-dev/pandas/pull/24039/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvZ3JvdXBieS9jYXRlZ29yaWNhbC5weQ==) | `0% <0%> (-95.46%)` | :arrow_down: |
| [pandas/io/sas/sas7bdat.py](https://codecov.io/gh/pandas-dev/pandas/pull/24039/diff?src=pr&el=tree#diff-cGFuZGFzL2lvL3Nhcy9zYXM3YmRhdC5weQ==) | `0% <0%> (-91.17%)` | :arrow_down: |
| ... and [121 more](https://codecov.io/gh/pandas-dev/pandas/pull/24039/diff?src=pr&el=tree-more) | |

------

[Continue to review full report at Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/24039?src=pr&el=continue).
> **Legend** - [Click here to learn more](https://docs.codecov.io/docs/codecov-delta)
> `Δ = absolute <relative> (impact)`, `ø = not affected`, `? = missing data`
> Powered by [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/24039?src=pr&el=footer). Last update [367efb2...1f3f4c9](https://codecov.io/gh/pandas-dev/pandas/pull/24039?src=pr&el=lastupdated). Read the [comment docs](https://docs.codecov.io/docs/pull-request-comments).
 lgtm. merge when ready @TomAugspurger @jbrockmendel  LGTM.  I might poke at simplifying down the road, but that shouldn't be a blocker. ok I merged the other one, so @TomAugspurger if you can rebase lgtm. ping on green. thanks @TomAugspurger 