BUG: Bug in DataFrame construction with nulls and datetimes in a list like
closes #15869
actually this is non-performant.

The issue is that it ends up looking at all of the strings, when we need to just test a couple to see if they are convertible. Not to mention this fails a couple of tests that have to do with us preserving ``date`` (which is annoying). I think this is fixed. boy user convenience is a PITA. ok I think its fixed now. As long as the test/benchmarks pass, then LGTM. This was a bigger effort than I thought it would be. @chrisaycock yeah a lot of this lower-level inference code is reasonable as we have quite a few integration tests, so refactoring stuff that I wrote years ago is pretty straightforward. But of course there are *lots* of cases and easy to break stuff (which the tests catch).

Down the road we will will be able to simplify things. For example ``datetime.date`` is not a first class type, so its *very* hacky when we infer from it (to maintain some compat). In the future, it *will* be more straightforward to do this (as we will have a valid first class type).

Further I have to think about whether we still want things like:

```
In [5]: Series([pd.NaT, '1 day'])
Out[5]: 
0      NaT
1   1 days
dtype: timedelta64[ns]
```

to work. It is reasonable & not too hard.

*this* is actually a bigger issue:

```
In [6]: Series([pd.NaT])
Out[6]: 
0   NaT
dtype: datetime64[ns]
```

as this is somewhat arbitrary. but this is for another time. # [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/15892?src=pr&el=h1) Report
> Merging [#15892](https://codecov.io/gh/pandas-dev/pandas/pull/15892?src=pr&el=desc) into [master](https://codecov.io/gh/pandas-dev/pandas/commit/e50d397efe31404802c55637793ea97850ac4e84?src=pr&el=desc) will **decrease** coverage by `<.01%`.
> The diff coverage is `100%`.

[![Impacted file tree graph](https://codecov.io/gh/pandas-dev/pandas/pull/15892/graphs/tree.svg?height=150&token=eZ4WkYLtcO&width=650&src=pr)](https://codecov.io/gh/pandas-dev/pandas/pull/15892?src=pr&el=tree)

```diff
@@            Coverage Diff             @@
##           master   #15892      +/-   ##
==========================================
- Coverage   90.97%   90.97%   -0.01%     
==========================================
  Files         145      145              
  Lines       49491    49495       +4     
==========================================
+ Hits        45023    45026       +3     
- Misses       4468     4469       +1
```

| Flag | Coverage Δ | |
|---|---|---|
| #multiple | `88.73% <100%> (-0.01%)` | :arrow_down: |
| #single | `40.63% <70%> (-0.01%)` | :arrow_down: |

| [Impacted Files](https://codecov.io/gh/pandas-dev/pandas/pull/15892?src=pr&el=tree) | Coverage Δ | |
|---|---|---|
| [pandas/types/cast.py](https://codecov.io/gh/pandas-dev/pandas/pull/15892?src=pr&el=tree#diff-cGFuZGFzL3R5cGVzL2Nhc3QucHk=) | `85.71% <100%> (+0.11%)` | :arrow_up: |
| [pandas/core/common.py](https://codecov.io/gh/pandas-dev/pandas/pull/15892?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvY29tbW9uLnB5) | `90.68% <0%> (-0.35%)` | :arrow_down: |

------

[Continue to review full report at Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/15892?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/15892?src=pr&el=footer). Last update [e50d397...6bf2148](https://codecov.io/gh/pandas-dev/pandas/pull/15892?src=pr&el=lastupdated). Read the [comment docs](https://docs.codecov.io/docs/pull-request-comments).