Ok, so "serverless" is just a buzzword that doesn't really have a good meaning. That's doesn't really matter. To me it's just easier and actually meaningful and objective to refer to services like AWS lambda as "Function as a Service".
To me it's like having one hand tied behind your back while someone else uses their hand to do what you'd have done with the one tied behind your back. It's cheaper, sometimes it works the way you want it to, but you always feel a bit restricted.
I get your feeling - I like to be able to ssh in as well, but then I see people I've worked for, and realise that to most of them having ssh access does no good, because they don't know how to troubleshoot over an ssh connection, and they don't want to have to know.
To them, losing that flexibility doesn't really matter, because they weren't doing it anyway.
For one example, I keep running up against wanting to delay an execution of one lambda from another. There are some truly horrible hacks out there to try and achieve that.
The irony is that a whole lot of the solutions are well understood; just not in the same environments. E.g. "enterprise" computing went through a whole cycle of building application services for small self-contained components with discovery and messaging in the late 90's that people seem to have largely forgotten as somewhere to look to at least for a laundry list of what kind of services are needed.
The "cheapness" argument is open to debate. So far the main argument I've seen for Function-as-a-Service offerings is that it's cheaper than just paying for a VM instance to run a dedicated service. To start off, a dedicated VM can cost about 5€ a month, which represents the absolute total saving that is supposed to be driving this discussion. Even if we ignore this fact, if you already have VM instances running somewhere then you certainly have enough computing capacity to spare to run these compute tasks without having to incur in extra charges per function call.
I once did some simple estimation of a cost of a VM inside our own infrastructure, and the costs was something around a euro or less.
A single, modern server can hosts a crapton of VM's, especially if you have a competent operations team inside your bussiness who builds tooling for it.