I can't agree with your rhetoric because it's based on the conclusion that you can lift more weight with a belt. I say if you do it's psychological. The strongest and fastest men in the Iron sports are the Olympic lifters. They are allowed to use one. If it increased their lift they would use it. If a guy my weight can lift 400lbs over head from the floor with out a belt why am I using a belt to knock out reps in the deadlift with 400lbs?
I can say without a doubt that I can lift more with a belt. If I had to estimate, the difference is around 5-10% but closer to 5%. Is some of it psychological? Perhaps. But I do know that my lower back feels a lot more stable with the belt on especially if I am using weights around 90% of 1rm or taking a higher rep set to failure or very close to it.
I am not 100% sure if weight belts are even allowed in Olympic weightlifting. Weight belts also limit your movement to some degree which is not ideal especially in the starting positions of the snatch and the clean and jerk.
I don't consider a weight belt a necessity especially if the person does not feel like they get very much out of it. But if someone has used it and saw a benefit there is no reason why it shouldn't be used as a tool in training (not a crutch).