CLN: remove util._doctools._WritableDoc
- [x] xref #25725 

Removes the metaclass ``_WritableDoc`` from the code base.
lgtm. ping on green. # [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/26164?src=pr&el=h1) Report
> Merging [#26164](https://codecov.io/gh/pandas-dev/pandas/pull/26164?src=pr&el=desc) into [master](https://codecov.io/gh/pandas-dev/pandas/commit/3e90d436e82ffafb9df287ebd9e5052387a251c0?src=pr&el=desc) will **decrease** coverage by `0.02%`.
> The diff coverage is `n/a`.

[![Impacted file tree graph](https://codecov.io/gh/pandas-dev/pandas/pull/26164/graphs/tree.svg?width=650&token=eZ4WkYLtcO&height=150&src=pr)](https://codecov.io/gh/pandas-dev/pandas/pull/26164?src=pr&el=tree)

```diff
@@            Coverage Diff             @@
##           master   #26164      +/-   ##
==========================================
- Coverage      92%   91.97%   -0.03%     
==========================================
  Files         175      175              
  Lines       52382    52374       -8     
==========================================
- Hits        48195    48173      -22     
- Misses       4187     4201      +14
```

| Flag | Coverage Δ | |
|---|---|---|
| #multiple | `90.53% <ø> (-0.03%)` | :arrow_down: |
| #single | `40.72% <ø> (-0.17%)` | :arrow_down: |

| [Impacted Files](https://codecov.io/gh/pandas-dev/pandas/pull/26164?src=pr&el=tree) | Coverage Δ | |
|---|---|---|
| [pandas/util/\_doctools.py](https://codecov.io/gh/pandas-dev/pandas/pull/26164/diff?src=pr&el=tree#diff-cGFuZGFzL3V0aWwvX2RvY3Rvb2xzLnB5) | `0% <ø> (-12%)` | :arrow_down: |
| [pandas/core/arrays/interval.py](https://codecov.io/gh/pandas-dev/pandas/pull/26164/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvYXJyYXlzL2ludGVydmFsLnB5) | `93.06% <ø> (-0.06%)` | :arrow_down: |
| [pandas/core/indexes/interval.py](https://codecov.io/gh/pandas-dev/pandas/pull/26164/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy9pbnRlcnZhbC5weQ==) | `95.22% <ø> (-0.03%)` | :arrow_down: |
| [pandas/io/gbq.py](https://codecov.io/gh/pandas-dev/pandas/pull/26164/diff?src=pr&el=tree#diff-cGFuZGFzL2lvL2dicS5weQ==) | `75% <0%> (-12.5%)` | :arrow_down: |
| [pandas/core/frame.py](https://codecov.io/gh/pandas-dev/pandas/pull/26164/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvZnJhbWUucHk=) | `96.9% <0%> (-0.12%)` | :arrow_down: |

------

[Continue to review full report at Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/26164?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/26164?src=pr&el=footer). Last update [3e90d43...09a5065](https://codecov.io/gh/pandas-dev/pandas/pull/26164?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/26164?src=pr&el=h1) Report
> Merging [#26164](https://codecov.io/gh/pandas-dev/pandas/pull/26164?src=pr&el=desc) into [master](https://codecov.io/gh/pandas-dev/pandas/commit/3e90d436e82ffafb9df287ebd9e5052387a251c0?src=pr&el=desc) will **decrease** coverage by `0.02%`.
> The diff coverage is `n/a`.

[![Impacted file tree graph](https://codecov.io/gh/pandas-dev/pandas/pull/26164/graphs/tree.svg?width=650&token=eZ4WkYLtcO&height=150&src=pr)](https://codecov.io/gh/pandas-dev/pandas/pull/26164?src=pr&el=tree)

```diff
@@            Coverage Diff             @@
##           master   #26164      +/-   ##
==========================================
- Coverage      92%   91.97%   -0.03%     
==========================================
  Files         175      175              
  Lines       52382    52374       -8     
==========================================
- Hits        48195    48173      -22     
- Misses       4187     4201      +14
```

| Flag | Coverage Δ | |
|---|---|---|
| #multiple | `90.53% <ø> (-0.03%)` | :arrow_down: |
| #single | `40.72% <ø> (-0.17%)` | :arrow_down: |

| [Impacted Files](https://codecov.io/gh/pandas-dev/pandas/pull/26164?src=pr&el=tree) | Coverage Δ | |
|---|---|---|
| [pandas/util/\_doctools.py](https://codecov.io/gh/pandas-dev/pandas/pull/26164/diff?src=pr&el=tree#diff-cGFuZGFzL3V0aWwvX2RvY3Rvb2xzLnB5) | `0% <ø> (-12%)` | :arrow_down: |
| [pandas/core/arrays/interval.py](https://codecov.io/gh/pandas-dev/pandas/pull/26164/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvYXJyYXlzL2ludGVydmFsLnB5) | `93.06% <ø> (-0.06%)` | :arrow_down: |
| [pandas/core/indexes/interval.py](https://codecov.io/gh/pandas-dev/pandas/pull/26164/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy9pbnRlcnZhbC5weQ==) | `95.22% <ø> (-0.03%)` | :arrow_down: |
| [pandas/io/gbq.py](https://codecov.io/gh/pandas-dev/pandas/pull/26164/diff?src=pr&el=tree#diff-cGFuZGFzL2lvL2dicS5weQ==) | `75% <0%> (-12.5%)` | :arrow_down: |
| [pandas/core/frame.py](https://codecov.io/gh/pandas-dev/pandas/pull/26164/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvZnJhbWUucHk=) | `96.9% <0%> (-0.12%)` | :arrow_down: |

------

[Continue to review full report at Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/26164?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/26164?src=pr&el=footer). Last update [3e90d43...09a5065](https://codecov.io/gh/pandas-dev/pandas/pull/26164?src=pr&el=lastupdated). Read the [comment docs](https://docs.codecov.io/docs/pull-request-comments).
 Green. thanks @topper-123 