Though I'd like to expand on this I'll try to make it short. I have tested the same scenario you explained where I started off adding 1k worth of tags in my Flarum's database. I was still able to select tags from the tag modal. Now, lets get down to the juicy parts. I dropped all records except the first tag that comes pre-inserted into Flarum at the time of installation of the tags extension that comes packed with it. Now for the fun part! I inserted all 121186 unique tags from the Stackoverflow dump you linked in your OP and it was bad news. PHP basically ran out of memory to where it is limited to 128M from the get-go if you didn't mess with memory_limit in your php.ini file.
PHP Fatal error: Allowed memory size of 134217728 bytes exhausted (tried to allocate 4096 bytes) in C:\wamp64\www\reflar.dev\vendor\illuminate\database\Eloquent\Model.php on line 476
But even after increasing PHP's memory limit, I was still thrown an error which was logged,
Maximum execution time of 120 seconds exceeded in C:\wamp64\www\reflar.dev\vendor\flarum\flarum-ext-tags\src\Tag.php on line 196
I assume there is a limitation because there is no pagination involved with the tags extension, it's basically fetching all tag records from the database and would affect performance if a limit wasn't imposed.
@clarkwinkelmann brought up a good point about pagination, but least we forget that even Flarum's packaged extensions are still in beta as well. There is more to be improved on and if anyone want's that many tags on their forum to compete with Stackoverflow, the more power to them (argumentative, yes, but you are probably insane). But the issue lies with performance limitations and what was stated above.
The only thing I would suggest is to add the "load more" functionality that some 3rd party extensions currently use to combat the absence of pagination (or currently shown in /all).
