Good question :-) My ideas below.
Different users are here for different reasons (as the other answer said). There is a split between users who are interested in conceptually interesting aspects of the technology, and users who are here to ask about problems they're encountering in their day-to-day work as developers.
The question I would ask is: "Are there enough interesting questions about the underlying concepts to keep the site healthy?" When these questions have been asked once, then they can't be asked again without being flagged as duplicates. Likewise, we can probably duplicate all "missing semi-colon" questions to the same previous question.
So I'd cautiously say that the site needs both the trivial questions about missing semi-colons and interesting conceptual questions to remain healthy and useful to the wider community.
If the questions are asked "badly" - e.g. poor English, or in an unclear format - then the community flags or edits them. If they're really bad and considered no use at all, then they get downvoted. The community gives its opinion of the value of a question by how it takes these actions.
Some specifics from your question.
The thing is that I find lots of people asking about losing transactions,
There are a few good answers that have traditionally been used to duplicate questions about lost transactions. For example: How can I reverse or cancel a transaction or recover lost ethers?
or about how to use their wallets,
These often get closed as "3rd-party software" questions. But I agree, the repeat questions about how to do basic things using Geth/Parity/Mist can add lots of noise to the site.
investment,
Definitely off-topic :-)
"my code doesn't compile" (And there's a site specially done for that)
I think we allow these because the Help Center specifically says that Solidity issues are on topic. If the code is actually Javascript - i.e. front-end code - then it's often okay to tell them to use Stack Overflow, and flag the question for closure.
and other not even technically questions.
Yes, sometimes it's difficult to judge what counts as technical or not. So sometimes good questions get closed, and bad questions get through.
I think in general (in my opinion - I'm happy for others to say otherwise), the definitions of what can and can't be asked as outlined in the Help Center are a good guide, and have worked so far, but often there are grey areas.
(I know I commented on your question about doing a Master's degree, and it is a good question :-) It's just if we start accepting opinion-based questions in general, we're likely to get lots of "what is the best way to implement MyCrappyToken" and "what will the value of Ethereum be in 5 years", etc. )
