Is it possible to add this feature - after user enter his/her question into the question text area, the website will auto insert some suggestive tags for the question and insert them automatically in the Tags field?
You the user are more suited to judging what are the best tags to put on your question (mostly) than an algorithm best-guessing through passes of keywords in your question.
If you have a question about cascading windows on a Red Hat setup, the weight of the windows tag, for its sheer use count, might have the system suggest that as a possible tag, even though it makes no sense to do so.
But the system doesn't read intent and will not be able to read your mind.
Statistical analysis is at a point where random's concerns are really not an issue. So long as the appropriate system is used, using the word "window(s)" in a question regarding Red Hat would not necessarily result in suggesting Microsoft Windows related tags.
Even if a simpler analysis system is used that does put up such invalid suggestions, using a "suggested tags" system would allow users to choose which tags to apply rather than simply auto-filling with possibly incorrect tags.
But statistical analysis really can tell the difference between a question about the windows on a Red Hat system and a question about Microsoft Windows, and so this question ought not be dismissed for this reason.
Further, the "you are the best judge" argument is invalid as well. Or course I'm the best judge, but a judge is only as good as their awareness of the issue and all possible judgements. I don't know what tags might be best suited to categorize my question effectively, and so it is possible, highly likely even, that there are related tags that I don't think of, or that the tags I do think of are lower-use tags that aren't actively followed by the other users. Having an "insider" seeing that my question shares a lot of keywords and phrases with other questions that deal with something that I have not tagged or explicitly mentioned in the question, and suggesting appropriate tags can be a great boon.
The point of a tag is usually to inform the system that my question applies to something that I might not have referenced explicitly in my question. The point of a statistical analysis-based tag-suggestion system is to ferret out additional relationships that I myself may not be thinking of.
I think the bigger issue is how to implement something like this in a way that does not slow down the interface or burden the server with a lot of extra processing. The systems I've seen (Zemify for blogs) tend to load a lot of JS that really make the interface drag. I would not be in favor of implementing such a system unless it could be done without significantly burdening the server or the clients.