That doesn't bother people a LOT?
Not really. I'm very rarely just playing Civ anyway as I'm either doing work at the same time, watching a movie, sending e-mails and Civ just sits in the background awaiting my next whim. I think most people will have something else going on around them to break the tedium, I would hope so anyway.
However, turn times as you've said are extremely long, even in the early game (T0-T50) they take far longer than they should for whatever little is happening.
Whatever the game is doing, it's not doing it well in that time and that is most likely to poor architecture or sequencing the AI turns rather than unifying them.
If it's processing each AI as an individual player rather than moving the units as individuals and then just running through city/civilisation objectives collectively, then its going to be repeating the same tasks over and over instead of running one smooth sequence, and I suspect this is where that slow down is coming from.
Maybe there is a reason it's done that way due to the higher level AI, but even if there is, the AI isn't of a level where you can actually appreciate that time.
This is indicative of Civ 5 overall in my view, the capability for greatness that would let you overlook it's flaws, but executed in such a haphazard fashion that those flaws become highlighted.
If it were my project, I'd pull it offline and go back to the drawing board. (Actually if it were my project it would never have been released until it had a list of known issues that had fixes in development.) But Civ 5 has all the hallmarks of too many chiefs and not enough indians in the software world, big sales, pretty graphics, lack of punch.
I seriously doubt they can patch their way out of this mess, it's an expansion at best or Civ 6 at worst. There are too many fundamental issues to just apply fixes to.
(I do love Civ 5, but it's clear that it's room for improvement is vast.)