Why not. U never peeled the expired one when have new?

I peel it many times when buy/sell my own car over the years.

go off peak hours less 10min job
Depends, on the prorated amount. Or if car is of larger cc its worth it rather than just let it rot.

you sold a car which still has hire purchase or you've setteled the hire purchase prior to selling to shitsome?
if it was still owned by FI, then need wait.

for refund, I just print statement with account number details enough, but I can tell you, it depends on the officer on duty also. So if you want safe & not waste time, maybe just ask bank if they can do so, as JPJ officer ask for it. If they refuse, then no choice, just proceed without.

Maybe i am understanding wrongly, but roadtax n insurance is not related for this case.

Insurance just call up insurer to cancel say due to sold vehicle & they will prorate refund if any.