The idea that you can only choose one is the root of the problem, IMO.

I'd say that the root of the problem is unfamiliarity with old typewriters, and the fact that the convention of tab stops defaulting to 8 spaces can so easily be overridden in the wrong way, yielding disastrous results.

Tabs are indentation, spaces are alignment.

The other way round that is. On the old typewriters, you could set stops for alignment of data skipping thus a fixed amount of spaces, mainly for filling out tables; whereas the indentation in typesetting e.g. at the beginning of a paragraph was done with spaces.