Honestly I'm pretty surprised there isn't more mobility for medical students.
It's incredibly common for law students to transfer to a higher ranked school after first year. We are talking like a third of the class in some cases. This is because top schools want to be more selective in terms of GPA and LSAT so they rank higher on US News, however if you take a bunch of transfers second year that doesn't affect your entering class stats. So more money, higher average first year stats = win for transfer students, win for school accepting.
(If you graduated in 2000 from law school and are going to disagree with me, you are wrong and I am right, this is how law school works now.)
Now the thing is the last two years of medical school are really a money maker for schools right? At least if you have a monster university hospital with tons of residents, you are going to be way under capacity when it comes to third and fourth year students. What's the real cost of having a student if you've got the hospital? It's like pure profit.
There's a pretty objective standard (step 1) for evaluating transfers. Step 1 and the first 2 years of performance are a much better indication of your work ethic/brains/commitment than premed crap is.
IDK I think it'd make sense for schools to have people transfer.
Honestly worrying about the DO prestige thing is kind of silly. Nobody should care, and at least it means you trained in the US. 20% of new doctors will be DO's for the classes starting now, it's not like the degree is going to stay obscure.
The easier thing to do if you are that worried about it is to lobby at the state level to change your state law to allow you to use the MD acronym for your degree. That already exists in a lot of states for MBBS and all the other foreign degrees out there (ie that dashing british doctor with an MBBS has MD on his business card and nametag). State legislators could change the acronym for DO in a swipe of the pen. Acronyms are a legal fiction, not something that has to be set in stone.