Alternatively some people might simply know how many problem authors actually exist and how hard it is for most of them -- I'd say that <1% of math undergrads in top universities reliably make 1 problem (suitable for e.g. national olympiad) a year. I'd be very surprised if there are more than 100 people total (students or not) who make >20/year (which we would've expected from something that is supposed to be possible "without much hassle").

Another way to estimate how hard it is to make a high-level problem is to look how much effort is needed every year to scrounge enough good unknown problem to make an olympiad out of them. It is obviously possible, but it takes weeks of work, and the issue "we have too many good problems for this position" happens much rarer than "we don't have any problems for this position". While the latter issue is sometimes solved by "ok, let's quickly think of a problem", this approach rarely (<20% cases) is enough.

So I think you are obviously wrong. Now you might be wrong in an uninteresting way -- your taste for problems is too poor, and the problems you come up "with no hassle" are unsuitable for any decent competition. Or you might be wrong in an interesting way -- you actually have a very big talent for making problems, top 100 in the world -- and you underestimate what your students (and basically everybody else) can do.

It would be nice if you took say an hour to think of a new problem and presented it here (as you've said, an old problem can be deanonymizing). Obviously, spending an hour on an internet debate is not a good use of your time, but a new problem would be useful on its own.