Most popular, sure, but most of the tanks and healers I see are geared well above LFR, and they're the ones that bottleneck queue times far more than 870 DPS that stand in the fire. I'm not saying the queues will triple, but it will have a noticeable effect, and it will make LFR harder.
Locking anyone to one difficulty is a bad idea. Let people run what they will; only the most tryhard amongst tryhards will consider that they ''have'' to run more than two difficulties, especially now that AP has such a bad return on time investment part the first few Concordance levels.
Oh, and it would also mean Normal+ raiders cannot obtain Augment Runes directly, a fairly important raid consumable. That's not good either.