"No, these questions should not be allowed. However, we could still allow 'softer' questions like 'Which bands could claim to be the greatest electronica act' or 'Who are the most influential blues artists."
Reasoning : There's rarely much point in a question asking what "the best" (or even "most successful") is, even if it's explicit (or implicit) that this should be based on measurable achievements. How, for example, do you meaningfully compare album sales for a band that were big in the 70s to a band that is around now, in a very different market? The same problem with comparisons would apply to other criteria too.
If the answer is so clear that even those difficulties don't prevent an answer - e.g. "Who are the most successful Irish rock band" - then it's probably not a question that really needs asking or adds much value to the site.
However, this site (like a number of other SE sites) has shown itself to cope well with questions that involve an element of personal assessment and judgement, as long as they still invite answers that are widely and generally valid rather than entirely personal. For that reason, I think we could cope with questions which invited answers that themselves would involve a discussion of the considerations.
For example, "What's the greatest metal band" is hard to give good objective answers to. However, "Which acts could claim to be the greatest metal band" invites more thoughtful answers that themselves could involve the discussion of whether AC/DC or Zeppelin are 'metal', how album sales can be meaningfully compared over time, and so on.