We had a funny situation with a fax couple of years ago.My bosses were opening a new company and because of some situation in the bank,they did request to fax the paperwork to them(email not safe, f2f wasn't an option).I asked my manager how is he going to do it,as he seemed quite puzzled. Eventually,he found one dumped behind all the cleaning equipment in the office. Dusted it off and managed to fax it somehow.This was for one of the largest banks operating in the UK. Fintech it's not.

Faxes are "signature-proof" for contracts. Scanned documents in an email are not.

That's the law being broken. Not the tech.

Why not scan a signed document and send it over an encrypted connection via the internet? Why do we have to send it over fax specifically?

Because the law was a special case for fax machines essentially instead of a generic one and they didn't understand the then very esoteric mathematical concept of converting arbitrary inputs to data and sending it in arbitrary ways.

We don't see laws today for unimagined hypotheticals like if governments if carrying a box with a stable frame of reference anchored wormhole inside that leads to a remote island with 1 ton of heroin is drug smuggling or not.

Hah, you'd be surprised at how much of US healthcare runs on Fax Machines (and 30 year old software running in win XP VMs...).

Fun-fact, a big German insurance company had something like that:

Customer send's fax printed out to paper, that paper got copied to 'real' paper for manual signature, that 'real' paper was then scanned and send digital (email) to a archive, where the printed out that digital contract to 'real' paper again (for the archive)

And the US is one of the only western countries where wiring money from one bank to another might mean that the originating bank prints a check, mails it to the receiving bank where it's typed in manually (hopefully correctly) and clears 6 weeks later.

Germany nailed that process in 1983.

What? LOL. ACH has been a thing for decades. Hardly anyone uses paper checks, and when they do, they are processed electronically.