It’s not a disaster if you can keep it under 1000, but I am not sure users will be able to comprehend that many categories. I dunno. Try it, see how it works, and report back in 6 months?
It’s good that you checked the page load times, though, that’s certainly advisable.
So why not dump them into their tag view and have that be their homepage? I’m not sure why that would be so problematic? Do they really need security here?