TOS screens just weren't animated cause it wasn't necessary. In ENT they showed that these screens can show animation. They just never had to in TOS.
I know, I was being sarcastic. Should have put a winky face.
In "The Cage" the monitors were animated in the background, but due to cuts in budgets after the pilot that meant they couldn't do little details like that for the regular production episodes. The bridge in the pilot is probably the best and most advanced it ever looked in TOS.