A smarter, and perhaps even more profitable way to approach this problem is "OK, we want almost everything that happens to customers to be a self-serve situation" and then make your (fewer) call centre employees highly trained troubleshooters who can figure out why _this_ customer wasn't able to self-serve and get that sorted for them. The result is a better customer experience (usually everything just works, when you need to talk to a human the human is an _expert_ who helps fix your problem, not a drone working from a fixed script) and it can be much cheaper if done right.
Definitely if you think of your product/ service as "premium" this is the correct model to have.
Lots of people simply do not like self serve. I get that companies want to cut costs, which is why we got endless telephone menu trees, then support web sites with crappy search, then automated telephone agents, then chat bots, and on and on. And the public has devised all these various tactics to skip that crap. I just want to talk to a damned human being rather than spend 10x the time navigating your poorly thought out Customer Avoidance Systems! Sometimes I need a drone and sometimes I need an expert. I have yet to see an automated system that could successfully determine which tier support I needed.
Often I prefer "self-serve," but sometimes I like to talk to a human who knows about the system that has created my problem, and can quickly fix it. That's why there are websites dedicated to showing people how to skip through phone menus and reach actual humans, even if those humans are soundboard operators paid almost nothing to make you go away.
Definitely if you think of your product/ service as "premium" this is the correct model to have.