The biggest issue this excellent exercise has is that it requires equipment, mainly the preacher station, or preacher "bench." For that reason, it highly unlikely to be a part of a home gym. There are many other equipment pieces you should buy before a preacher curl - a regular bench, pullup bar, power rack to name a few.
The second problem is the popularity. If you are a member of a crowded gym, more likely than not the preacher station will be occupied 24/7 by curl bros. Also, those bros are unlikely to use towels and are highly likely to wear tank tops, and their sweaty armpits will go in full contact with the pad, which is far from pleasant. We say it again, don't be that guy, just put a towel on the equipment, do the exercise, and clean when done.
The third problem is that for some people, but very rarely, preacher curls cause pain and discomfort in wrist, elbow, shoulder or other weak areas.
But don't worry, if you can't do preacher curls for whatever reason, we got you covered. The next section will have some great alternatives.