Except that not every mathematician will actually have done Taylor Series. Algebraists, logicians, topologists and graph theorists, for example, may very well not have done analysis to that level.
This is actually more reasonable than expecting an analyst to produce basic group theory proofs.
This was in Australia in the early 80s, and to this day I think of TSs as sort of obvious. But I did Pure Maths, and I think TSs are more emphasised in applied where you use them for approximations, etc.
Which aspects of your undergraduate real analysis course did you not find obvious (if any)?
But this was 32 years ago, and while I've used calculus in one form or another constantly, I've never had to do anything "interesting" with Taylor Series. Now looking back I'm hard pressed to say what was easy and what wasn't, what was obvious and what wasn't.
It would actually be interesting to go be an undergraduate and see what is obvious now with the years under my belt, and what needs to be thought about hard.
I really, really, really want to know an example of that.
(Philosophical logicians do not score as examples of this).