Well I wouldn't be so naive to say the "LFR" was the sole reason behind a staggering and unexpected loss of 1.3 million subs, but It wouldn't be wrong to say it hasn't had an adverse effect.
LFR has completely changed the dynamics of raiding. Since the start of the expansion its pretty clear to say that a lot of the major population of raiders are simply not interested. Its carried on from the last expansion, however, Dragon Soul was comparatively much easier than either of the last 2 tiers.
Guilds have simply quit after hitting small road blocks cause raiders have not bothered showing up. I've heard from a couple of guilds on my old server about the lack of interest from people in raiding. The #1 guild (world 200) on our very small-medium recently transferred servers. There is simply no incentive to raid Normal mode right now and that was a significant majority of the raiding population. Sure you could raid, Heroics are there for those looking for a challenge, but that is not where a majority of raiders spend their time raiding.
Now this same group have found easier access via LFR with out a conflict to their schedules. This has resulted in folk simply not giving a care to come prepared to raids or LFR. Even trying putting a PUG together is frustrating since a lot don't bother gemming and enchanting.
Not only that, but the gearing up process currently is terrible design. Blizzard wants LFR to be the catch up content returning players have to go through to gear up. Considering Justice Points gear is below Heroic Dungeon gear and since you can't even buy last tier's gear via Justice Points, its become very frustrating especially considering how the loot system works in the LFR. You either have a chance to win something or you don't. You can't even trade drops. And considering you can go for weeks with out winning anything, its hard catching up.
However, there are other reasons as well. I felt Cataclysm simply gave the player base more reason to roll alts than any point of time in the game. Cataclysm didn't really much going on at level cap. The Fireland dailies got boring soon enough and it was easier to catch up. Cataclysm was the time I levelled all my alts. WTLK had a perfect balance of raiding, dailies and things to do at level 80. I enjoyed the separate raid lock outs.
Currently for any returning player to the game or a new player, the task ahead seems very daunting. I know how over whelmed I fell on returning to the game. The amount of dailies required is simply staggering.
On the other hand you have PVP completely imbalanced at any point in the game. Even Cataclysm honestly felt much better. PVP right now all revolves around CD burst. BoTs are at an all time high and Blizzard hasn't seem to crack down on them. Sure they changed a few things but its still not solved anything.