I agree with your first two paragraphs especially - the issue is the trolley problem is designed as a thought experiment for exploring a single idea.

The issue with its misuse is that it gets presented almost as proof in itself that there is no third option, nor an infinite future of consequences. The trolley problem was never and could never apply to real life, because life is necessarily far more complex, culpability and obligation are just two of like a million relevant factors.

It's as absurd as using Schrodinger's Cat as a way to justify any actions in real life - It's a thought experiment designed to think about one single idea in a different way; it has practically no relevance to reality.