If you are going to give a positive review (No Action Needed or vote up) then yes, you need to check other answers to make sure that it is not plagiarized. In this case it is also worth to check other answers from the poster to make sure that they don't copy their own answers from other questions instead of closing as duplicate.
If you are going to give a negative review then there is no need to check other answers. When you see a post like "I am having same problem, have you resolved it?" you don't need to look at anything else to make a decision, you just vote down and flag it.
And there is no need to check other answers if you are going to skip (note There is no shame in using “Skip”).
In my experience vast majority posts in Late Answers review are (unfortunately, but probably naturally) worth negative review or skip and because of that it is convenient that review page shows just one answer under review.
In rare cases when I intend to give positive review - yes, I open the question in separate page to check for more details. Since it happens infrequently, it's not a big deal.
And even if review page would show other answers, this still wouldn't suffice for positive review because as mentioned above, in these cases I also check other answers posted by this user to make sure that they don't copy their posts instead of closing as duplicate.
Summing up, to me it would probably be less convenient overall if review page would be cluttered by other answers.