People who do heavy BB Squats...

Denigrations aside, the pad keeps you from having adequate control over the bar and it's harder to feel whether the bar is in the right position. If after a few weeks of squatting a couple of times a week, you're still bothered by it, the bar is probably in the wrong position. Power lifters and Olympic lifters use different styles altogether but either way, the bar shouldn't be that uncomfortable.

The other issue with squats is whether to use a belt or when to use it. Oly lifters prefer to use it selectively becasue using it at all times prevents the core from benefiting from squats (and any overhead movement). Most Oly coaches recommend using the belt only when you get to 85-90% of your max as a routine or if you really need it at other times (like if you're extra sore or a masters lifter). Unbelted deadliftts, squats, front squats and overhead squats will strenghthen your core as much as or more than anything else, provided that you do it wisely.