There are basically two types of hosting:
- "Shared hosting", where you upload files though their control panel and they handle everything. You just get what they give you, and if you don't like it then you don't really have options beyond switching to a different plan (if they have one) or switching to another hosting provider.
- "Give you a VPS" where you have the responsibility to administrate the server. You can install what you want, and configure however you want, but it's up to you to do so.
The second is what systems like certbot are for. For the first kind of hosting, they should just be handling https automatically (but for some reason not all do).
If you have control over DNS or able to upload a file to the web server, then it is possible to run something like certbot in "manual mode", get the key & certificates, and send it to your provider. You'd need to do it manually every couple months, and it's the most complicated, error-prone, and insecure way to do it (if you're sending the key around to somebody). But it's not the way I would do it.
With some shared hosting setups, you can get away with CertSage which is a PHP script that can try to integrate with the control panel. You still need to do it manually every couple months, but it's at least keeping the keys on the system and you might not need to involve their support each time.