Say I want to know every game where the main character is a soldier, or every game with random level generation, or every game with orchestral music, etc. Is this an appropriate sort of question for arqade?
No, these types of questions are off-topic.
Questions that ask which games or other products meet specific criteria are off topic. We primarily deal with questions about playing games, not about which games to play or historical trivia. We make an exception for identifying games based on an audiovisual artifact from the game in question.
No, it is not.
Arqade is focused on QA, and what you're asking for is an open ended list. In that case, how are users to select "correct" answers? Should each game that meets the criteria be posted as its own answer? How do you know when the list is "complete" and worthy of answer accepting?
Unfortunately, our format does not suit such an open question, and were it to be asked here, would be summarily closed and deleted.
Even if the other two reasons given so far (asking for games that fit certain criteria; asking for an unbounded list) weren't enough reason to close it, those examples are also an absolutely enormous set: each of those could be answered by lists many thousands of items long, that grow every day. Such a question could be closed as "too broad", in addition to the more urgent reasons.