Shared hosting
It's a bit bad if a host isn't supporting one of the free cert systems, chances are they aren't updating their control panels, cpanel/whm/plesk has had it for 2 years or so which probably covers the majority of hosting. ISPConfig has it, and a quick google of some of the others seems to come up with results too.
If your host isn't updating control panels which control the system, it makes you wonder what they are doing with the rest of the system.
Even for the home grown control panels, adding a few form fields, then having a cron job that checks for a letsencrypt install request for the domains in question, then running the command which does everything for you isn't exactly rocket science, after that add it to an auto renew cron and job is done.