Followup to #20347 (str_cat)
cc @h-vetinari 

Some requests for simplification. Most of the complexity seems to be in the code inferring what kind of regime we're in (one or more alignable objects vs. one or more unalignable objects vs. mix). Being strict here (after deprecating) or requiring additional user input may be worthwhile from a maintenance perspective.

- [ ] https://github.com/pandas-dev/pandas/pull/20347/files/3f77b80b4ca7c8b04894b00bc08e980b62b97b97#diff-4627140a96de4a6390883e22e983f1b2
- [ ] https://github.com/pandas-dev/pandas/pull/20347/files/3f77b80b4ca7c8b04894b00bc08e980b62b97b97#diff-4627140a96de4a6390883e22e983f1b2
- [ ] https://github.com/pandas-dev/pandas/pull/20347#discussion_r185459889
- [ ] https://github.com/pandas-dev/pandas/pull/20347#discussion_r185460287
- [ ] https://github.com/pandas-dev/pandas/pull/20347#discussion_r185460641
