Usually proxying can work for https connections - by letting the proxy terminate ssl. But then you really need to trust the proxy's ssl implementation, and it probably also breaks standard security ui like viewing the cert.
The SSL implementation is the least of your problems. You’d need to have a private CA on your system that creates certificates on the fly. How do you secure that proper. You’d also have problems when reporting SSL errors between the site and the proxy to the browser because from the browsers PoV, the connection looks good.
Definitely it has its problems.