Allow sites to opt in to the following behaviour: When asking a question, do not show new users the tag field. Instead, let the question start as untagged (just as if the question was just migrated to the site with no tags carrying over).
When new users edit their own questions or suggest edits to other questions, they can edit the tags as normal. They are not required to tag their own questions when editing though.
First of all, I am fully aware that this would be a horrible idea many sites, such as Stack Overflow, where at least one tag (e.g., the programming language) is usually a straightforward choice. This is for sites where this is not the case, and tagging is particularly difficult for new users, for example:
On language sites, many tags reflect grammatical categories and other linguistic concepts that many new users are not familiar with. At times, identifying the grammatical categories is what the question is all about. Moreover, some tags have special rules that do make sense but are not immediately obvious to new users, e.g., noun may be reserved for the grammatical properties of nouns, but must not be used if you are asking about the lexical meaning of a noun.
On sites about social topics (The Workplace, Academia, Interpersonal Skills, …), it is difficult for new users to discern what tags are actually essential and not incidental to their question – if they approach tagging like this at all. For example, a PhD student asking a question on Academia has a very high chance of tagging their question phd, even though somebody at another career stage might as well have the same question.
On these sites, users also tend not to specialise on particular tags very much, but rather select questions they care about from all questions on the site. Tags therefore do not have the function of quickly bringing a question to the attention of those who can answer it. (They are still relevant for searching and similar.)
Another relevant observation is that experienced users tend to properly tag untagged questions very quickly, while they may not touch questions that are already tagged, no matter how badly. This effect can even be enhanced by making untagged visually stand out.
Thus, on the sites in question, there are hardly any downsides to leaving questions by new users untagged, while it very likely stimulates better tagging.