I see a lot of questions being marked as off-topic for various reasons. Should more focus not be placed on helping these people to get their question trimmed to bring it under the guidelines of the website?
Ideally, we should be educating new users than fixing their questions for them. It is the OP's responsibility to ask or answer a question that conforms to site rules. So I usually point them to the list of our FAQs or to a more specific one like this. A determined user will often work with moderators and other users to have his/her question reopened so it can be answered.
In my opinion, close votes should be used as a last resort, if multiple attempts to bring the questions on-topic do not work.
Close votes are just another way to flag problematic questions. And even if a question does get closed by mods or by voting, it's not the end of the road as it says here:
Is closure the end of the road for a question?
Definitely not. Closed questions can and should be edited to improve them and address the reasons why they were closed in the first place. Once this is done you might need to either flag the question for moderator attention or raise a meta question to bring it to everyone's attention so it can get the necessary views that might translate into reopen votes.
This will also help increase the number of questions asked per day without any decrease in quality.
Why do we need to (somehow) increase the questions asked per day? Who are we trying to beat? :)
More importantly, this would reduce any discouragement new people face when their questions are put on-hold etc.
No matter what you do, some people find the site rules too harsh and eventually leave the site.