You could always just pay for a “private server” - virtual servers are not so expensive these days.
Shared hosting comes with many shared “things”.
One-size-fits-all will usually feel a bit short (or long) to most - as few are at the “exact average” fit.
My domains are registered through IONOS/1and1.
My cPanel does have the SSL/TLS icon, and yes all those sections are in there.
As a side note, I’ve noticed AutoSSL running on two occasions in the last few days when I happened to be looking. If they have a limit on issuing certificates, couldn’t they just have it run a little less frequently?
AutoSSL runs on a regular interval and also on certain events (like domains being added).
That it’s running is not necessarily related to Let’s Encrypt’s rate limits.
After all, AutoSSL might run, and decide that nothing needs to be done. No rate limit used up on the Let’s Encrypt side.
The two concerns are independent.