CLN: Address some TODO comments
- [x] closes #23098
- [x] tests added / passed
- [x] passes `git diff upstream/master -u -- "*.py" | flake8 --diff`

I am technically moving some public (non top level) helper functions and making them private, but I don't think it warrants a depreciation.
Hello @mroeschke! Thanks for submitting the PR.

 - There are no PEP8 issues in the file [`pandas/core/common.py`](https://github.com/mroeschke/pandas/blob/cc8cc4c6910db697966c838ef220f17016ade20c/pandas/core/common.py) !

 - There are no PEP8 issues in the file [`pandas/core/frame.py`](https://github.com/mroeschke/pandas/blob/cc8cc4c6910db697966c838ef220f17016ade20c/pandas/core/frame.py) !

 - There are no PEP8 issues in the file [`pandas/core/generic.py`](https://github.com/mroeschke/pandas/blob/cc8cc4c6910db697966c838ef220f17016ade20c/pandas/core/generic.py) !

 - There are no PEP8 issues in the file [`pandas/core/indexes/api.py`](https://github.com/mroeschke/pandas/blob/cc8cc4c6910db697966c838ef220f17016ade20c/pandas/core/indexes/api.py) !

 - There are no PEP8 issues in the file [`pandas/core/indexes/timedeltas.py`](https://github.com/mroeschke/pandas/blob/cc8cc4c6910db697966c838ef220f17016ade20c/pandas/core/indexes/timedeltas.py) !

 - There are no PEP8 issues in the file [`pandas/core/internals/blocks.py`](https://github.com/mroeschke/pandas/blob/cc8cc4c6910db697966c838ef220f17016ade20c/pandas/core/internals/blocks.py) !

 - There are no PEP8 issues in the file [`pandas/tests/frame/test_mutate_columns.py`](https://github.com/mroeschke/pandas/blob/cc8cc4c6910db697966c838ef220f17016ade20c/pandas/tests/frame/test_mutate_columns.py) !

 # [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/23208?src=pr&el=h1) Report
> Merging [#23208](https://codecov.io/gh/pandas-dev/pandas/pull/23208?src=pr&el=desc) into [master](https://codecov.io/gh/pandas-dev/pandas/commit/b54e20b4c05727268857dc8cd8acd065f70c6048?src=pr&el=desc) will **increase** coverage by `<.01%`.
> The diff coverage is `90.47%`.

[![Impacted file tree graph](https://codecov.io/gh/pandas-dev/pandas/pull/23208/graphs/tree.svg?width=650&token=eZ4WkYLtcO&height=150&src=pr)](https://codecov.io/gh/pandas-dev/pandas/pull/23208?src=pr&el=tree)

```diff
@@            Coverage Diff             @@
##           master   #23208      +/-   ##
==========================================
+ Coverage   92.19%    92.2%   +<.01%     
==========================================
  Files         169      169              
  Lines       50950    50943       -7     
==========================================
- Hits        46975    46972       -3     
+ Misses       3975     3971       -4
```

| Flag | Coverage Δ | |
|---|---|---|
| #multiple | `90.62% <90.47%> (ø)` | :arrow_up: |
| #single | `42.27% <52.38%> (ø)` | :arrow_up: |

| [Impacted Files](https://codecov.io/gh/pandas-dev/pandas/pull/23208?src=pr&el=tree) | Coverage Δ | |
|---|---|---|
| [pandas/core/common.py](https://codecov.io/gh/pandas-dev/pandas/pull/23208/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvY29tbW9uLnB5) | `98.34% <ø> (+0.89%)` | :arrow_up: |
| [pandas/core/generic.py](https://codecov.io/gh/pandas-dev/pandas/pull/23208/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvZ2VuZXJpYy5weQ==) | `96.84% <ø> (+0.18%)` | :arrow_up: |
| [pandas/core/indexes/api.py](https://codecov.io/gh/pandas-dev/pandas/pull/23208/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy9hcGkucHk=) | `99% <100%> (+0.08%)` | :arrow_up: |
| [pandas/core/internals/blocks.py](https://codecov.io/gh/pandas-dev/pandas/pull/23208/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW50ZXJuYWxzL2Jsb2Nrcy5weQ==) | `92.9% <100%> (-0.01%)` | :arrow_down: |
| [pandas/core/indexes/timedeltas.py](https://codecov.io/gh/pandas-dev/pandas/pull/23208/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy90aW1lZGVsdGFzLnB5) | `90.74% <100%> (-0.03%)` | :arrow_down: |
| [pandas/core/frame.py](https://codecov.io/gh/pandas-dev/pandas/pull/23208/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvZnJhbWUucHk=) | `97.02% <75%> (-0.1%)` | :arrow_down: |

------

[Continue to review full report at Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/23208?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/23208?src=pr&el=footer). Last update [b54e20b...0e1ceaa](https://codecov.io/gh/pandas-dev/pandas/pull/23208?src=pr&el=lastupdated). Read the [comment docs](https://docs.codecov.io/docs/pull-request-comments).
 thanks!