I don’t think LFR is a good fit for TBC.
First, there’s no gear designed for it, or difficulty setting designed for it. TBC is not as difficult as retail, but some fights would be not very LFR friendly without changes. Hydross needs tanks in full resistance gear, Vashj/Kael are probably too difficult outright, certain fights almost require specific tanks (pally for AoE, Warrior for spell reflect, etc). TBC raid comp is usually designed around stacking buffs and debuffs to complement groups, and LFR is very bad at this. It’s also a famously melee unfriendly expansion.
Second, attunements (at least until they are removed) make previous tiers required to progress through to get to current content. LFR would change how that works, and create a very different feel. Whether this is good or not is subjective to the player, but I would rather have attunements play out where they are important for a while, and as the content becomes older, they get removed as they originally did.
Third, there is a very healthy pugging scene on classic, and I expect that to survive to TBC. I don’t think that players will be as inclined to manage these runs if LFR exists.
Fourth, the community issues everyone keeps bringing up. Yes, I understand your opinion, but it is your opinion, no more valid than anyone else’s.
Fifth, I don’t think it’s a good idea to pull systems from future expansions in general. It takes the excitement/anticipation of a feature away from the expansion it came from, and if there are negatives to that system, no matter how much you personally don’t care about them, adds them to an expansion that didn’t have those negatives. I think blizzard has generally been pretty restrained about this, with some smaller exceptions.