Is there any way to "request" that the asker reviews the latest answers and considers accepting another answer?
Nope, the asker is the only person who can accept an answer. The votes do indicate what the community agrees with, but the asker is the overall say. You can comment below the question however to bring light to the highly upvoted answer. The user will then get notification of a new comment and might come back to review the question. It is their call because it is their problem and their choice on what solved it or what they liked.
When you answer the question at all, a message is generated in that user's "Recent Events" feed. So they are already informed.
The other side of the issue is a question of whether or not the community can really determine what answer it was that helped the OP the most, and the fact is that the cannot. The community can vote up answers to indicate which answer they this is the most useful in general. So if your answer is more generalizable, or more abstract, thereby making it applicable to more situations, then you answer will be highly voted up. It doesn't mean that you answer was 'more helpful to the OP'.
Votes mean 'useful in general'
Accepted means 'useful to me'
There are also cases I've seen where the most popular answer was not the best answer and the OP had chosen the correct answer even though it had fewer votes. I like the current system since it can balance somehow between both extremes. The community can correct OP errors and the OP can correct community errors.
As noted in other answers, "getting accepted" and "getting upvoted" are different concepts. In case your answer outscores (by 2x) a good (at least 10 upvotes) accepted answers, you'll be awarded a gold "Populist" badge.
