Bartlein states that the 5 R is not any more accurate than their 4 groove.
Popularity drives sales.
I have more than a few of 5R in various calibers and one 3R in a 6 Dasher. They are all accurate and easy to clean like all custom barrels. As to whether or not one is more accurate than the other, I could not say that.
Bore uniformity from one to the other, with perhaps a .0002 choke toward the muzzle is what I like the most. 4 groove and 6 groove of top brands will not fail you, and I have never had a bad three groove from several makers.
Getting a good straight chamber in line with the bore is way up on my list vs. groove design or number of grooves.
When I was shooting Benchrest Competition, there was a saying going around, that if a guy showed up with a Wheel on the side of his scope, and he won the match, then at the next match, everyone would have a wheel on their scope.
I have ran into two very good gunsmiths that will refuse to chamber a 5 R barrel due to the increased chance of reamer chatter, and I am not expert in this at all. My 5 and 3 R's came off without a hitch.
I think that it is nothing short of amazing how one group or type of barrels are popular with Benchrest shooters, then another with Tactical shooters, etc.
Note, I don't think that Remington his hammer forging their barrels now, they are made in Alabama. They bought all the barrel making equipment from what is now X caliber and moved that equipment from Montana to Alabama. X caliber folks did not want to move, and they started their own company, now making some fabulous barrels.