Huts don't have that great of an effect on the game. One could argue that re-rolling starts, using mapfinder, turning off barbs, or picking creampuff opponents has a much greater effect.
In most games, even if you pop a critical tech, you only save a few turns in the long run. For most of the VC's it's a trivial effect. Religious victory has a slightly larger effect because the game is so short.
A large amount of the time, Huts provide a significant amount of Wealth. Sometimes they provide a few early Technologies. In my opinion, many Players should learn how to Win the Game with using Tribal Villages. In particular, many Players depend on the early Hut hunting for huge amounts of Wealth (for the early Game). This is mainly why I'd like to see more HOF competitions forbid use of the Tribal Village option.
Perhaps, I overstated my case against Tribal Villages. However, you may be understating the effect of Huts. Getting early free Wealth from Huts can allow a significant stretch of turns at 100% Research running a significant deficit. It's not just the free Technologies that I'm against.
In the lower levels, Huts provide Workers and Settlers and frankly many Players should learn to Play without the Hut crutch. In the recent Settler level Gauntlet, I seem to recall more than one Player popping six Settlers. That's not insignificant in my opinion; it really ruins any semblance of Strategy that might otherwise exist at the lower Difficulty levels.
In the final analysis, popping something good or bad from a Hut is a matter of pure Luck. There's no best Strategic/Tactical way of Popping other than the trivial tactic of using a Scout rather than some other unit to maximize Wealth provided. There is also luck in winning/not winning combat, but in combat tactics used can greatly effect the outcome. There's no such redeeming quality in a Hut. The Hut is superfluous, chaotic Game element whose only function is to "spice up" or "spoil" the Game; its worst than eye candy, because of its detrimental effect on the Game. The only redeeming quality of the Hut is that its fun to pop, except possibly when Barbarians are on.
In your comparison of the Tribal Village option to other things allowed in the HOF, only No Barbarians is another option. I'm not sure the other items you mentioned are a fair comparison.
Remember that this is only a request to have all Huts off for the next HOF Challenge Series. I'm not requesting a ban on Huts, although I'd shed no tears if they were banned.
Sun Tzu Wu