Fax isn’t encrypted. What keeps it alive is just inertia.
As for why your insurance company won’t take emailed photo, that probably has more to do with whatever system your insurance is using for their backend.
Email content can be end to end encrypted by GPG and S/MIME as well as through a few other standards. Email in transit can be (but not always is) encrypted via TLS.
The reason encryption is not default is because (I think) of backwards compatibility. E-mail originated at a time when almost nothing electronic was ever encrypted, including the username and password you used to log into a system with. Most of the encryption we use of today has simply been “bolted on” to standards that were already in place at the time and it did take a few tries to get it right.
When the internet was first getting started, few people, if anyone, thought it would become as invasive (possibly the wrong word) as it has become. Everyone on the net knew each other. They were friends, why would they ever need to hide anything from each other. /s
That and the early systems couldn’t really spare the processing power for encrypting and decrypting things.
That sounds like an overloaded server. If you not willing to put up your own server, you might try a few of the smaller public instances.
There is only so much traffic the larger instances can handle, and right now it seems like everyone and every community is on only a handful.