The difference between losing your teaching job for being a nonce and losing your peerage for ‘any crime’ (as suggested by the OP) is in the former the conviction would directly affect your ability to do the job.
A closer reflection might be to occlude from parliament those who have been convicted of a certain subset of crimes. Perhaps the requirement to sit in the House should be revised to allow only those peers without said convictions; we could do something wooly and English like calling it “upstanding character” maybe.
Personally, I think it’s a stupid system anyway, and the whole idea of peerage is loony. However, I fundamentally don’t agree that personal and professional lives should be intertwined; footballers who get suspended from playing because of extramarital affairs, for example.