I can't speak for others, but here are the reasons I strongly dislike them:
They're low-effort. You can ask the same question for any numbers, any sources, and any set of allowed operators. What makes any individual puzzle of this type special?
They're often ill-defined. Many of these questions allow "any standard operator" without specifying what exactly counts -- there are a whole lot of possible operators. Are trig functions allowed? What about hyperbolic trig functions? Double factorial? Is the "$F_\bullet$" function, giving the Fibonacci sequence (e.g. $F_7 = 13$), allowed?
One frequent ambiguity is in concatenation - are you allowed to concatenate the starting digits, or any results along the way? Another is if the puzzle is defined in terms of characters - many forms of mathematical notation reuse the same symbols for different meanings. If you allow parentheses and fractions, is the Legendre symbol allowed? Without any explicit rules, there's no way to tell for certain what an expression means. Mathematical writing, like all writing, is context-dependent.
They're not single puzzles. A single one of these would be answered in minutes, so questions often instead ask for you to create a whole range of numbers. This doesn't make the puzzle any more interesting, it just makes it take longer to answer -- and it often means that the end result will be split among multiple people.
Puzzles should have a definitive solution that "puts the puzzle to rest" - both in general, and specifically because of this site's format.
They aren't "narrow" enough to be good puzzles. The best puzzles are ones where there is a particular clever solution that the setter has in mind, and the puzzle will require you to find that one to solve it. In formation-of-numbers questions, the OP often doesn't really have any particular solution in mind (or even know if it's solvable!).
And all of these problems are only compounded when the question is posed as an optimization problem. If you say "find the solution with the least number of operators", or something to that effect, then...
- any ambiguities in the problem statement are extremely harmful, because it's impossible to tell whether a solution is the best answer or invalid.
- you'll get a bunch of different answerers not only filling in the gaps, but also incrementally improving on other answers.
- it's more likely that you don't actually have a clever solution in mind, and so the solution won't be interesting.