Are you old enough to be online?

You can construct a trolley problem to justify anything you want. It's about the constraints that the person who posed the question chose. You don't really get to choose in a trolley problem. The constraints choose for you. In the real world, our options are not so constrained and the outcomes are not so clear. As such it is useless for actually figuring out what to do.

The trolley problem is a useful basic philosophical experiment to get people to think about things and reflect on constraints, assumptions, and values. And often the best response is in fact "fuck these constraints and assumptions!"

So the trolley problem is not bullshit, but it is very very often misapplied in a bullshit or bad faith way, for example last year in the US I saw a lot of liberals uncritically and unironically appeal to "the trolley problem" to rationalize voting for the party that was committing a live-streamed Holocaust. They were using it to absolve themselves of the responsibility to think about and own their moral judgements, and that is the sort of misuse that a lot of people balk at.

Because it implies utilitarianism is the best option by oversimplifying the problem. For example in your example you gave zero details on the situation.