I am a mathematics researcher. I agree with most of what you say, but
> Reviewers are pushed to accept papers instead of rejecting them, because a rejected paper makes no money
The only pressure I ever get is from editors (i.e., other mathematicians, who make all the final decisions), if I'm taking too long and they want me to hurry up.
If a representative of the publisher attempted to pressure me for any reason, then my response would be less than polite.
Occasionally I have gotten review requests from "pay to publish" journals which will publish pretty much anything, and which don't have any credibility within the math community. These, I simply delete as spam.
Just occasionally? I get at least 3-4 of those daily! They've become seriously annoying, and confused senior professors around me often fall into the trap.
It's possible for pressure to exist at a higher level. The editor simply stops asking reviews from people who reject papers above some threshold rate. Or at even a higher level, the journal replaces the editor who maintains a too low an acceptance rate.
These pressures are harder to notice, without population level data.
I reject the invitations too, but the fact is that they exist, there are (many) people who do them, the papers are published, they come up in searches, and the whole thing becomes a muddy mess.
Most people say “we’ll just don’t read/cite them” but the fact is that there is no clear red line; it’s all foggy. In order to look at a paper and say “I will not read you because you are crap” you need to spend some time with it, and if you have 2000 of them, that translates to a lot of wasted time. The reason why journals are supposed to do serious peer review was exactly so that we don’t have to do it ourselves.
> Reviewers are pushed to accept papers instead of rejecting them, because a rejected paper makes no money
The only pressure I ever get is from editors (i.e., other mathematicians, who make all the final decisions), if I'm taking too long and they want me to hurry up.
If a representative of the publisher attempted to pressure me for any reason, then my response would be less than polite.
Occasionally I have gotten review requests from "pay to publish" journals which will publish pretty much anything, and which don't have any credibility within the math community. These, I simply delete as spam.