Apart from the fact that the implicit claim in the question is not always correct (but seems to be true, at least in my field, most of the time); and in addition to the fact that doctoral thesis reviews and grant proposal reviews can sometimes be more effort than reviewing a paper (but reviewing a paper in mathematics can be enormously difficult, if you feel the need to check that everything claimed is true!), maybe it has to do with the following:
I would expect an "average" researcher to submit about as many papers papers as they review (at least in the same order of magnitude). Sometimes even PhD students are asked to review papers.
In contrast, almost every researcher has a PhD and needed reviewers for their dissertation; but probably less than 10% of them will ever review someone's else dissertation?
Similarly, the average researcher will apply for a couple of grants (starting as students already), but probably only the more/most senior researchers are asked to review grant applications (at least in my field, I assume).
Accordingly there might be some sense of balance for paper review: I expect others to review my paper, so it is only fair that I review one paper of someone else. But this balance is broken e.g. for proposals: One person is asked to review, in one go, 80 proposals submitted for a grant. So looking at a single proposal might be less work than a paper review; but doing 80 of them might be more work; and the person will not submit 80 grant proposal over their career, so it seems unfair to expect them to do the work without any incentive.
Remark: It is a bit of a mystery to me that free peer review (in particular for highly profitable and expensive journals) works at all. Of course there are some people that claim they learn a lot from reviewing papers (but they could do so by just reading the same papers on arxiv, right?), and some people might get some other benefit out of it (they might have an agenda to reject their enemy's papers, or accept their friend's, or force people to include references to their work, etc). But I think most researchers do reviews (which can really be a huge effort) in an honest way, motivated by the notion of fairness described above. While this is nice, it seems somewhat unusual that an industry can be kept alive just by the spirit of fairness and cooperation against the participant's self-interest... But this is a question that has been discussed at length already, see e.g. Why don't researchers request payment for refereeing?