I think it's fine to post questions that don't show any research, only if:
- it's equally fine to choose to ignore them
- it's equally fine to choose to downvote them
- it's equally fine to choose to comment asking the OP to improve them
- it's equally fine to ultimately close them when they have been hanging around with downvotes long enough to be clutter on the site
- it's equally fine to use them as examples on meta of the kinds of questions that are considered poor
If the possible reactions to this option are in any way objectionable, then it just shouldn't be done.
I've said it before, so I'm aware that I'm repeating myself here, but I'm certainly not interested in answering such a question unless I have some special interest in the topic.
To answer your supporting arguments each in turn:
-the best majority of the ~800 questions posted here so far don't show any research
This is called a red herring. It means nothing except that a lot of questions show no research effort.
- as a patient it is sometimes difficult to know where to start looking for trustworthy information
If someone can find an SE site and figure out how to post a question, they probably know how to google something, or explain why they can't.
- it might be better to state a simple question rather than adding some unreliable sources in the question.
Every mistake is an opportunity to learn. If someone really believes in a source and goes to the effort of posting it, I think that's still a better question.
As Hercules said, the gods help those who first at least try to help themselves (that's a paraphrase of his actual mythological words.) Not that answerers are gods or anything. We're all only human.