Tags of this sort are known in SE parlance as "meta tags", i.e., tags which don't actually describe what the question is about, and instead describe some other ("meta") aspect of the question. As a general rule, since over a decade ago, meta tags are strongly frowned upon; see the original blog post for much of the reasoning for this. In short, there is a very strong consensus that meta tags are bad and should not be used except for very limited exceptions with very tightly defined use cases.
On this site, we have very few meta tags. The most common one is homework-and-exercises, with resource-recommendation, specific-reference, research-level and popular-science trailing behind. The first three have very clear reasons for existing, and they are tightly codified. The other two are, honestly, in decline, and should maybe be phased out.
The specific tag that you've proposed was discussed back in 2012 in Can we have a level-of-question tag please?, and similar tags were discussed in
Can we encourage the "research-level" meta tag? What about a "popular" tag? and
Would having a second set of tags relating to the nature of the question make sense?.
For additional background, it is very much worth looking up past discussions of meta tags on a network-wide level at Meta Stack Exchange.
So, as a general rule:
yes, if the user asking a question requires a specific level for the answers, then this should be indicated in the question text itself. If the OP does not do this, or if it's not obvious from the way the question is posed (which is almost always the case!), then it is good practice to encourage OP to do so, and to edit it in if OP provides the information as a comment.
Moreover, there already is an incentive (i.e. an additional +15 in rep from answer acceptance) to post answers that OP can understand. And, on the other hand, if any answerer wants to post an answer outside of that domain (say, because they feel that it would be useful to a wider audience), the can do so $-$ and should remain able to do so.
And, all that said,
no, it is not a good idea to encode this information as a tag. This type of tag is extremely difficult to maintain and enforce, it has very little usefulness in practice, and the descriptions tend to be to vague to be applicable even in single examples, let alone consistently (and usefully) across different questions by different users.