I was under the impression that you can MITM HTTPS, it just requires the client to trust the proxy (by installing its CA). It's mostly used in corporate environments for monitoring & blocking, but it should work for caching proxies too.
https://rasika90.medium.com/how-i-saved-tons-of-gbs-with-htt...
Yes it seems they call it SSL bumping
Even when done "correctly", this breaks so, so much stuff on a typical developer on Windows set up. Ask me how I know.
I have corporate VPN that forces this. Basically a bunch of programs break because they come with their own trusted CA list
Ironically everything works fine if I VPN in from home, or from a phone hotspot. But in office connected directly to the network, no dice. We just switched back to 5 days in office after trialing 2 days WFH the last couple months, so that's actually where it matters most.
Try to make this MITM caching work consistently for all the computers (phones iot etc) of your home.
Then think about doing the same for a school.