Well, no one is saying they have to "give anything up" - just that they don't have exclusive use of it.
Copyright law and public domain are meant to balance between creators controlling their creations, and the greater good for the public/arts in general. They were not designed for corporations to exploit in perpetuity, they were designed to give authors (the actual human beings) and their heirs ample time to profit. And in this case, they didn't call the modern updates to the laws, extending the time period enormously, the "Mickey Mouse Act" for nothing, as Disney spent a pretty penny to make it all extend this long. And the creators heirs are long gone from the company.
The issue that is now pressing is when these laws were written, there was no concept of the modern marketplace where something that is copyrighted can be perpetually trademarked at the same time. They know there is no way in heck that either side of the political aisle is going to get behind any copyright extension again (the 90 years is already bordering on the absurd).
This is why Disney has been promoting all the "vintage Mickey" merchandise and likenesses the last few years. To prove that they still use "that version of Mickey" for merchandising should they ever need once the actual copyright is gone, as one of the provisions of keeping a trademark in perpetuity is that you continue to actively exploit it. It could be argued that if they didn't, then they weren't exploiting "that Mickey", so they would no longer have a trademark on it. (It goes into the weeds a bit there, especially when you take into account the precedent set by the Superman cases, where a character isn't a single entity, but different versions of that character hold different rights based on when they were created/began use.)
The truth is, it isn't really going to affect that much. Basically, if you want to make homemade cartoons of Mickey from that era and distribute them on, say, YouTube or wherever, there is nothing Disney can do about it. But Universal or Warners isn't going to start making Mickey shorts to compete with Disney.
To be honest, it's not really Disney that has much worry in terms of being hurt financially by someone else exploiting the characters at this point. It's really going to be a bigger issue in another eight or ten years when the comic book characters start to go to public domain. Marvel is set for a good long while in most cases, but it's Superman/Batman/Wonder Woman that are next up on the block. Given that fan films (some of pretty high quality) are already being made regularly, particularly for Batman, once people can actually make them and sell them for profit, it's going to be a very different (and interesting) ballgame.