100+ terms in any taxonomy slows down post updates?

The bigger the table, the more work adding a term becomes. There’s nothing unusual about it, it’s a matter of scale.

Consider this:

I’m at a pie eating contest. Once I go past 100 pies in a specific contest, eating a new pie takes a lot more time…

To diagnose what is slowing things down, you will need to monitor what runs on the various update hooks, and run profiling tools. It could be caches being regenerated, etc, poorly configured mysql+apache setup.

Eitherway, things will slow down as you ramp up the number of items in your WordPress install, and the plugins and features you have turned on will compound that effect.

Also consider doing a repair and optimise on your tables.