"The new server should handle the toots of its users. Maybe they should charge them for it. "
If the alternatives are either pay to move your posts or leave them on the old server with a redirect for free, I am guessing the vast majority of people will choose the redirect.
It's not even just about the storage costs but the time.
I have almost six thousand posts on my account. If I move servers, how will the new server's admin have time to go through all those?