I did this with my wife’s 2005 Honda minivan, and also with my 2012 Subaru Forrester. Brought back both of them. No special inspection required. And no issues getting them inspected each year.
Check with your insurance company. My insurance company did not care when I asked him about it, which I was surprised to hear. But I think the only potential issue is they may not offer you comprehensive coverage (coverage for your own vehicle if you do something that is your fault, or if the other driver is not insured) anymore.
On both my vehicles it was a seamless process. I did not have to go to the DMV or switch plates or anything. The insurance company may have sent me some papers to sign, and then they took care of everything. They may have sent me a new title in the mail. I can’t remember.