You are simplifying it too much. If I am facing a 3x open raise and I 3-bet it to 13x that doesn't even begin to make me pot committed. Even if I make a 50% pot C-bet on the flop I am still not committed.
This would be true in tournaments where you get committed sooner due to the fact that there is no such thing as top up and that stakes aren't deep most of the time.
I'm not over simplifying, and it is true in cash games too. It is relatively less accurate, but that doesn't really matter.
theoretical instance: Hero and Villain, both have 100bb's.
Villain bets 3.5 bb's Hero raises to 10.5 bb's Villain calls.
The pot has 22.5 bb's, and the Hero and the villain have 89.5 bb's which gives us an SPR of around 3.9. That is a relatively hard spot to be in, because its easier to get bluffed at, not bad but quite what we want.
So, lets say we raise it to 12bb's instead of 10.5. Now the pot is 25.5 bbs and we have around a 3.4 SPR. Its a small change in bet size, but we can commit ourself in that spot.
we can CHOOSE to commit ourself in that spot. The reason is that there is enough money in the pot that we can make basically 2 pot sized bets and be all-in. That means we can get our stack in for value with TPTK. AK is a great example of a hand like that.
Now we can then choose to uncommit ourself if we see that things are turning badly (we have TPTK and there is a straight and flush possible). Once you can get your stack in with 2 pot sized bets you have set yourself up to be committed.
You are setting yourself up to play for stacks, and about a 3.5 SPR or lower is what you want for TPTK type hands.
If you can get an SPR of 2 or lower then you are in a good spot, you get your stack in fast and easy and then you are essentially unbluffable. The hand takes care of itself, set yourself up for victory by raising. You are more likely to get yourself into a crappy spot by calling a bet with AK and getting TPTK than you are if you 3bet. 3betting makes your life easier.