Allow dtype promotion in Series[ExtensionArray].__setitem__?

[TomAugspurger]

Pandas typically allows for __setitem__ to change an object's dtype.

In [5]: a = pd.Series([1, 2])

In [6]: a[0] = 'a'

In [7]: a
Out[7]:
0    a
1    2
dtype: object

This typically won't work for ExtensionArrays:

In [8]: b = pd.Series([1, 2], dtype='Int64')

In [9]: b[0] = 'a'
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-9-a40f9ead6ccf> in <module>
----> 1 b[0] = 'a'

...

TypeError: <U1 cannot be converted to an IntegerDtype

So, two questions:

1. Do we want to allow this kind of type promotion for EA-backed series?
2. If so, how do we design it? Presumably something like ExtensionArray._can_hold_item(item: Type[scalar, Sequence[scalar]]) -> bool. Or maybe the return could be True for "I can hold this", False for "No, raise an exception", and something else (a dtype?) for "Yes, but astype me to something else first)".

I'm needing to work around this for DatetimeTZArray, since we do allow setting with a new timezone (upcasting to object).

In [8]: ser = pd.Series(pd.date_range("2000", periods=4, tz='UTC'))

In [9]: ser.dtype
Out[9]: datetime64[ns, UTC]

In [10]: ser[0] = pd.Timestamp('2000', tz='US/Central')

In [11]: ser.dtype
Out[11]: dtype('O')

[h-vetinari]

This seems like it might fit the method pandas.core.dtypes.cast.maybe_promote, which does effectively that. It's quite broken and needs a major overhaul anyway - I've started by writing a docstring and tests for it in #23982

[mroeschke]

Similar issue encountered in #26041 (comment) with loc[:, col] instead of __setitem__ (probably hits the same path)

I'm +0.25 to coercing to object. It'd be great if the assignment "just works", but the object dtype tends to surprise people it seems.

[jbrockmendel]

xref #39584