I started realizing the benefits of not using a belt about a year ago, so I gradually stopped when doing lighter sets of deads and squats.
There is a trade-off though. By putting pressure on the belt with your stomach, you will be able to use more weight with squats and deadlifts, even if your core is already strong.
The problem I had when I first started not using a belt was that my core wasn't as strong as it should be for the amount of weight I was using for squats and deads. I lightened up on the weight, but that of course affects the benefits that my posterior chain and legs would have gotten with heavier weights (with the same rep scheme).
I think of it sort of the same way I think of deadlifting from a deficit compared to Romanian deads. One has a longer range of motion but you have to use less weight, the other has a shorter ROM but you can use more weight.
With a belt you can add a little more weight and that's one way to change things up; just remember that your lower back and stabilizing ab muscles aren't getting worked as hard so when you use a belt you can add core work (like standing military presses without a belt).
You can even rotate which exercises you use a belt with so you get more weight with some, and more core work with others.
All in all, I'd say that most gym-goers use their belt too often at the expense of core strength.