Why are you talking about tournaments? Also TT plays well in position in a raised pot even without the need to hit a set. If we 3bet there are 3 things that can happen:
1) Villain can fold and we win 5bb (assume blinds fold).
2) Villain can 4bet and we lose 12bb (3bet size was a bit large imo) because we can't call a 4bet.
3) Villain can call with a range that crushes us.
He'll fold more often than either of the other 2, probably even enough to make 3betting profitable, but only marginally so.
Now if we flat, we see a flop (95% of the time the blinds don't 3bet) for 3.5bb. We can call a flop bet on almost any flop (probably about 5bb). We can take the pot on the turn a lot of times with a bet and on boards where we don't think betting the turn if checked to is best we can get to SD rather cheaply or get an additional value bet in from smaller pairs that might give up to a turn bet.
As to what range I am 3betting here, KK+/AK/some junk. Basically hands I am willing to play for stacks with preflop and bluffs. No need to do that with 22-QQ (QQ is close with some villains but I don't think it is with this one).
I mentioned tournament play because of this earlier comment:
"As said earlier if I had just called the initial raise I could comfortably play a small pot in position with a medium strength hand or even better, flop the set and try to get stacks in from there."
I think that's a great way to think about small/med pairs, facing a LP raise in the early stages of a tournament. When blinds are relatively small, and there isn't much money in the pot, it makes sense to see a cheap flop, flop a set, and double through. In that situation, I'd always call.
I don't ALWAYS think that way in cash games. After a LP raise, there's 4.5BB in the pot. That's enough to scrap over, sometimes, with or without the cards. In addition, with the raise coming from LP we're facing a wider part of our opponents range and maybe even a steal.
I read/understood the rest of your points and did some filtering:
3bet= 3.72 BB/Hand
Call= 5.92 BB/Hand
However, I didn't 3bet nearly as many times as I thought I would have in this situation (26%). So, the results are kinda skewed (and from a very small sample size).
Going wit that, I think you are probably right that calling is more profitable than 3betting here.
But, 3betting is still profitable... Taking table dynamics, our current image, and our opponents current temperament into consideration; I'd like to soften my argument to:
We should probably just call most of the time but not automatically so.