Host offers SSH but won't accept external SSL certs. CANDO?

Yes, it’s relatively common. Hosts have historically made money by selling additional services such as SSL certificates. Many will charge you per time for adding a certificate ( which every few months, starts to add up). some will insist that you need to “upgrade” or “get a dedicated IP address” in order to be able to add your own SSL certificates.

On the other hand, there are plenty out there who will either let you upload / install your own certificate, or even better actively support Let’s Encrypt and make it automatic for you. Have a look at Web Hosting who support Lets Encrypt for a list of some hosts who do this - you might find something that fits your requirements there.