Regarding "the pros and cons of such a feature," note that Math.SE (like all StackExchange sites) emphasizes Community Moderation. Much as all Users are equally entitled to ask about the various mathematical topics, all Users are equally permitted to attempt answering any posted Questions, or to propose improvements (edits) to posts so long as the intent of the original author is preserved.
Mathematics is particularly opposed philosophically to "authority" as the basis for proofs or solutions to problems. While no human enterprise is devoid of "appeals to authority", when invoked in mathematics without the ability to demonstrate claims by rational argument, it is disparaged.
A proposal of a feature for "assigning" Questions to particular Users will immediately meet that headwind. Users differ in their topical abilities at exposition and insight, but the author of a Question should know what they are asking well enough to discern for themselves "good and sharp answers" for that particular subject. Thus an OP should judge the Answers received rather than pre-judging who best will provide a response.