That seems kind of harsh?
I'll then read the introduction. If I don't have sufficient expertise to referee the paper, I'll decline the request. If I do, then I'll see what the authors have accomplished. If, in my judgment, this doesn't rise to the level that the editors asked for, then it doesn't take me a long time to decide this and say so.
Conversely, if the introduction does impress me, then I will want to check the proofs in very close detail. In this case I will commit to writing a detailed report in the future.
It's quite common for papers to be declined from individual journals; it's happened to me plenty. There are tons of other journals out there; you can submit somewhere else. And when I decide that a negative report is called for, I write it right away, so as to not keep the authors waiting forever.
You can always put work up on arXiv if the goal is priority or distribution. Peer review is, in principle, designed to ensure that work is new and true (and that what is new is true). It’s not meant to fix flawed work, but to make good work better.
...I fear however that my hopes are in vain
I've had many paper rejections, none because of false or uninteresting claims but almost all because "it's not good enough for this prestige journal" or "it's too specialized for this journal". I expect a certain number of those, because I submit to reach journals now and then and hope I get a reviewer and editor that like the work :) If I wanted certain publication immediately I'd submit to lower-tier journals first, which I have also done when I just needed something out.
Economics and linguistics also publish their own journals which costs some money but significantly less than Elsevier's subscriptions (I believe linguistics' is 300 USD per year). There's probably enough momentum behind middlemen-run journals that prevents this from happening more en masse.
We tend to think of journals as being run by their editorial boards -- i.e., by scientists in our field. The publishers are in the background, not taking a very active role, simply skimming off truckloads of money in the process. In particular, peer-review requests tend to come from scientists whom we know at least by reputation, and often personally.
When I spend serious time peer-reviewing a paper, it will be on a quality paper on a subject that I enjoy reading about anyway. (If I get asked to peer-review a paper that looks uninteresting to me, or something outside my interests and expertise, I'll either decline the request or write a quick report recommending that the paper not be accepted.)
It's interesting work, it's important for the health of the field, it helps me support other researchers in my field (if I like their paper and give it a positive review), and it helps my own reputation (the journal editors are often bigshots). From this point of view, it's a win-win-win-win.
Finally, paying for peer review doesn't make much sense because the time required is highly variable. I might take between 20 minutes and 30+ hours to review a paper, and I wouldn't necessarily expect the editor to be able to predict how much (even within an order of magnitude) in advance.
However, I see no reason why high-profit publishers should be able to insert themselves as middlemen and engage in rent-seeking behavior. I hope we figure out a way to give them the boot, and then continue approximately as we have been doing.