This is an awesome thread, I really hate some companies who put out certain items as these amazing features when others are passing them on free, SSL the big example. I mean it's ok to say hey we give free SSL, join us, but don't email me if I don't buy an SSL I will lose ranking, get hacked, etc.
I hate that kind of marketing. (Cuz im the type of guy that will go get Cloudflare or letsencrypt, or Comodo just so your stupid sales tactic won't pay off.)
For me things that should be there:
SSL - especially if you were giving it for free prior to chrome and firefox changes.
Access to your Zone records :O( this one tees me off when its not there to just has a mx record in it)
The ability to move your domain ( remove registrar locks ) Might be there for security reasons.
Backup utility that Cpanel provides and r1 soft restore, I guess some hosts remove this to save space?
Exim Access
Rouncubes backup utility
Cphulk Access
Error logs
They're probably more and my answer is based on working on different client webservers, some are good, some are bad some are decent.