I agree with your first point. I'm not sure if that qualifies as "cynical", but it's definitely true. It's critical to winnow down these huge classes before upper-level coursework begins.
> Well they get paid for it, don't they? Either from the government or student loans, most schools aren't doing it for free.
No, they don't get paid nearly enough to justify the time of the people involved. With weird, rare exceptions, anyone teaching one of these lecture courses at a major research school (i.e. any public school) makes most of their salary -- and earns far more money for the school -- by doing research. Maybe it all pencils out in aggregate (e.g. the teaching staff is a loss, but at N=250 students you break even, or whatever), but I suspect that isn't true in general.
Teaching these courses takes up so much time that you barely get anything else done for a whole quarter/semester. That's hard when you have a lab of people to manage and an active research program. Schools usually manage it by indenture, coercion, voluntary mutual sacrifice, or all of the above.
There are different reasons for investing in it despite this fact, but the big one is the unwritten rule that "this is a University, and this is what we do". Sometimes you take a loss to support the wider team. In this case, it's pretty bad marketing to have a university without a pre-med pathway, just like it's bad marketing to have a gym without a climbing wall (or whatever the fad is these days).