Why are many obviously pointless papers published, or worse studied?

• Some poorly-run institutions pay people to publish papers. The pay is not based on the quality of the papers, only the number and possibly other useless information like the indexing of the paper.
• Some poorly-run institutions require students to publish papers to get degrees, but the quality of the papers is not adequately assessed.
• Some people do not realise their papers are pointless.
• Some of the papers that are pointless in your opinion are not pointless to other people.

There are also many good papers.

I used to laugh about a pair of pointless papers. The authors had (independently) proved that Polish notation not only makes formulas of propositional logic unambiguous without needing parentheses but continues to do so if the formulas are written in a circle, so that one can't immediately see where the beginning and end of the formula are. Later, I learned that this result provides a key step in some combinatorial arguments, including a proof of the Lagrange inversion theorem for formal power series. (The people who provided that proof of the inversion theorem were apparently unaware of the connection with logic.) The moral of the story is that I should not have judged pointlessness by the original purpose of the work but should have taken into account possibly unexpected applications elsewhere.

Let me propose two counterpoints to your question.

First, what one finds silly someone else doesn't. I'm amazed that my most cited paper is basically aspirational and does not contain any strong result; on the other hand my best work is not cited very much at all. In fact there is usually an inverse correlation between my ranking of my own work and the number of citations. Hence what I find sillier others do not.

Second, I realized some years ago that some papers are just "silly" because they are - in some sense - practice. I (or a collaborator or a student) had to publish papers under tight timelines, or under some pressure for a grant or something other deadline. As a result, these are compromise. I used to worry quite a bit about this until I visited the Musée d'Orsay in Paris: there you will find that, before making their "big work", the masters practiced on "études", a series of smaller tableaux where only some small elements are different. It all looks very incremental. There is one series in Orsay where three "études" show the same haystack with different hay colors, different backgrounds etc.

Now... I don't want to defend people who constantly and only publish "silly" papers, but I will add the following anecdotal evidence: a lot of the more incremental stuff is just to keep you going to a better, more properly formed, final non-silly paper. I see this quite a bit of that as a referee for journals or grants: there are 3 or 4 papers in a series, and they eventually open the way to something more substantive and unexpected.

Sometimes not... you realize that the small "silly" papers already comprise all there is to say; the better researchers will move on.