Those aren't third-party HTTP proxies, they're local HTTP proxies. If you want to do it locally, then you're paying the CPU / RAM cost yourself, not to mention

Those aren't third-party HTTP proxies, they're local HTTP proxies. If you want to do it locally, then you're paying the CPU / RAM cost yourself, not to mention doubling a lot of the work (the page needs to be parsed / interpreted / JS executed by the proxy, and then again by your browser) -- so why not just do it in the browser? If you want to do it third-party, you need to trust this third-party because they're terminating the TLS connection for you (not to mention being fundamentally incompatible with TLS 1.3)