fax machines!!!!!!
my time travel comment was supposed to be a joke
IIRC it's considered to leave a better paper trail and if it goes through you know it's there (as the fax machine either connects and completes or doesn't) and not been eaten by a spam filter either at the client, or at the isp/mail provider.
Also cheques are/were less likely to be paid into the wrong account, one of my friends works in a solicitors office and works on property sales, he's got some hair raising tales about how easy it is to send very large sums of money to the wrong person because you've entered a digit wrong on the computer or the recipient has transposed two numbers when telling them, and until recently there was no automatic check/feedback from the system to tell you the account name didn't match the number, and that's before the issues with fraud (people actively target solicitors to get the money sent to a different account things like sending instructions via an email address that looks like it's from the real client but isn't*).
I think things have improved a bit now, but IIRC it's only in the last few months that all UK banks have implemented a warning if the account you're sending money to doesn't match the name you've given it (and even that isn't fool proof, if you consider how common some names are).
A lot of the "out of date" practices used by some professions are there because they offer a level of safety, or checking that simply isn't there with newer methods, or has only just been adopted so there tends to be inertia, especially when if you can't prove you did everything correctly you are on the hook for very large sums of money, and possible malpractice/sanctions from a governing body.
When the NHS got hit by the ransomeware that took down many systems, hospitals and doctors were still able to continue working in part because they do tend to keep at least the more recent/important documentation partly on paper filed away.
*Email is horrible for security, as most clients don't tell you if the email address that is shown matches the one that was actually used by default, so spoofing the from field is pathetically easy.