I feel like we should normalize what often happens in the UK where former Prime Ministers often serve in the House of Commons after their time in office, at least for a period. It would be interesting to have a former President in the House of Representatives - John Quincy Adams became a very productive member of the House after he was president. We sort of have this situation with Pelosi I'd argue and she's still a big voice. It's a good opportunity to still have a big impact on the issues you care about.
IMO it's generally seen as unseemly for expresidents to get back into politics through an elected role-a good example IIRC is Hoover who tried to get another nomination at the 1936 and 1940 conventions but failed both times.
