There indeed are some partners in social dancing that are pain to dance with. They soon learn that if they don’t improve people will not dance with them. Some get feedback given to them.
From what I read on DF, AT mores, values, practices, culture in this are so different from ballroom, it would be useful to stop comparing them.
I always thought and was told ballroom spends more time on teaching technique, balance, timing than social dances. In other social dancing threads we routinely discussed the unpleasant dances. The unpleasant dances aren’t routine. They are exceptions unless you are stuck in a low quality scene. I have done a lot of social dancing. Some times four or five times a week for several years. Most partners at intermediate level and above don’t have flaws that could lead to harmful dancing or injuries. Accidents can happen. They are far and few in between. Hanging on to a partner is considered very negatively in social dancing.
Social dancing and pro-am competition dancing do not equate. Not that one is superior to the other, they're just different, and require different talents and skills from the professional.
Many pro-am ballroom teachers work very hard at getting their students to do the work necessary to manage their own body weight well. That can be a long process, if it happens at all. Whether the student actually learns what is taught is on the student. Oodles of pro-am student competitors simply want to be moved, not to move themselves; to be held up, not to hold themselves up. Many pro-am teachers comply, and haul their students around the studio and/or competition floor. But mostly, they don't social dance
for fun.
One of the amateur men who social dances with me, who routinely hangs on me, pushes my shoulders around* and wrenches me into uncomfortable positions, asked me, "Why is it that when I social dance with my teacher, she makes me feel like a great dancer, but when I dance with you, I feel like a bad dancer?" or WTTE.
I told him, in plain English, "You're paying her. You're not paying me. Of course, she's going to make you feel like a great dancer. From me, you get honesty." Apparently, it had never occurred to him that if you pay someone to dance with you, that person has an financial interest in making you happy.
*To wrench this back on topic: speaking of injury on the dance floor; if I do several dances with him in the course of a social, my shoulders ache for days. Extra attention to shoulder work with the Yamuna balls helps.
Isn’t there any minimum criteria of how good an am should be before a pro lets them enter competition?
Nope. That's why ballroom competitions have so many levels, including "newcomer," and judges have different expectations for dancers at those levels. Much depends on your teacher. Mine would not let me compete for three years after I started taking lessons from him, and during those years, he warned me against telling people who my teacher was (pretty sure that last was a joke, but I was so intimidated, I complied).