While Nemesis had many flaws, the OP only wants to know if the movie would have been better without the Remans, so I'll attempt to answer that question.
First of all, I don't think the problem was the existence of the Remans per se. For decades we all knew of the existence of Remus (or Romii, or RomII depending on your take of the Neutral Zone diagram in "Balance of Terror"), but previous fandom simply believed that this second planet was also populated by Romulans as well. That's certainly what the early Diane Duane novels implied. Since there was absolutely no canon information up to that point about the Remans or Remus, if someone wanted to come along and reinterpret the Remans as being some kind of Romulan lower-class slave race that does all the grunt work in the Empire, that would have been fine with me.
The problem was the actual portrayal of the Remans in the movie. Contrary to KingDaniel's assertion that he thinks that space vampires are cool, I thought the Remans were not cool. They were basically Nosferatu rejects with costumes straight out of a Tim Burton Batman movie. They looked like vampires for no other reason than that they were supposed to be "EEEVVVIIILLLLL!!!!!" They were complete cardboard villains, and even the great Ron Perlman was completely wasted in this film. I think that at some point between the idea for this movie and what was eventually filmed, we the audience were supposed to feel sorry for these poor creatures because they were enslaved, but nowhere did I feel the least bit of sympathy for them for the reasons stated above. And to top it all off, the film didn't even have the courtesy to make it clear about just what the Remans' origins were. Were they originally Vulcans like the Romulans? Were they aliens that were already living on Remus when the Romulans arrived 2,000 years ago? If they were originally Vulcans, how could they possibly have changed to look like they do in only 2,000 years? Why would they have developed fangs?
Nor did I ever feel that Shinzon really gave a crap about the Remans despite what he said about wanting to liberate them, but of course that has more to do with Shinzon's problems as a character than the Remans themselves.
I do think the Remans were necessary to the overall story, but that they really needed to be presented in a completely different way, and have the audience care more about them. But the film didn't do either of those things.