Rooting out fundamental disagreements with hypothetical questions
If two people have an irreconcilable disagreement about the trolley problem or the red/blue button question, it's likely there are broad categories of more realistic questions they will never be able to reach an agreement on. This sort of thought experiment helps to distill the essence of those questions and drill down to potentially fundamental disagreements on morals and ethics and other decision making factors.
Unfortunately, many people can't see this connection. They perceive these questions as totally divorced from real life, often a waste of time, and potentially even harmful to discuss in isolation from real world details. This applies not just to famous questions and problems, but also to topical hypotheticals (or even non-hypotheticals) that tease a single issue out of a larger scenario. If you're one of those people, I'd like to convince you otherwise.
Consider trying to choose an ice cream flavor to share with a friend, at a bespoke flavor ice cream shop where every serving has many ingredients. Or perhaps trying to buy a car, or plan a road trip. You keep vetoing their choices, and they keep vetoing yours, and neither of you can figure out the other's requirements. Fortunately in these examples, you probably have some convenient shared vocabulary that you can use to convey “I'm allergic to stonefruit” or “I need a large trunk” or “I want to visit some museums along the way”. But, imagine if you didn't, if the thing you were trying to coordinate on was deep and complex enough that it would take a philosophy degree to explain and understand the underlying positions and factors. How would you proceed?
A quite plausible path forward in those scenarios would be to choose some options that aren't actually under consideration, but which differ in fewer ways, to attempt to narrow down the important factors. “Hypothetically, if we had to choose between just the two options of cherry garcia with pecans or cherry garcia with chocolate chips, which would you pick?”. It doesn't matter that those two flavors aren't on the list, or that you wouldn't pick them even if they were. What matters is that you've narrowed the choice down to a single factor / axis / variable, and the answer to this question will elicit some information that might have been difficult to impossible to deduce from the more complex choices. You will quickly find out about everyone's pecan vs chocolate chip priorities, and you'll probably also learn about nut allergies, without needing to discuss any other factors at the same time. This will allow you to narrow the scope of all the remaining considerations. Even more effectively, this might tell you that the larger scale problem is impossible. If one of you has a nut allergy and the other has a chocolate allergy, and every item on the menu has at least one of those, then you'll quickly discover that you can't share an ice cream order at all.
That last part is the most useful aspect of philosophical and moral thought experiments. If you can narrow the question down far enough to expose a fundamental disagreement in your positions or beliefs, you can disqualify a much larger category of discussions. There's no point having [some] complex discussions about hospital management decisions if you disagree about the trolley problem; you won't ever be able to reach an agreement on certain real world issues.
My favorite example of this is regarding taxation and individual rights to others' labor. There are virtually unlimited depths to that debate. However, before we spend any significant amount of time on that, I want to find out if you support taxation of the wealthy to feed orphans. If so, then our differences are matters of degree and details. If not, there's no point discussing finer details; we are never going to agree on anything downstream of that fundamental position. This is true even if just taxing some people to feed orphans is not a policy that would ever be under actual consideration.
I'd love to hear about some hypothetical scenarios or thought experiments that you don't believe can lead to useful real world conclusions. I consider it a fun game to come up with realistic scenarios that depend on a given distilled question.