I would have guessed they'd shrug at the first sign of trouble, swap it out with a known-working mouse and mark the ticket resolved... unless all the replacement mice were thin plastic too, I suppose.
It would bother me until I figured something out.
I suppose a good office-computer mouse in 1990 would cost $100 ~ $200 (say $350 today). In that case, yes troubleshooting it for a day would make sense, especially if it's not an isolated problem.
This is not a sensible comparison to make. Support staff have a lot of free time. They have to, because they're support staff -- if they were always busy, then whenever a problem arose, it would be impossible to get support.
So to have the IT department playing with the mouse is unlikely to cost the company anything. If something comes in that's more important, the mouse problem will be put aside. If they have nothing better to do, they can play with the mouse.