First of all, the Church is not allowed to change the teaching of only men becoming priest. However they can allow priest to marry in The Latin Rite. That is something they can change. Other rites are allowed to get married.
I have mixed thoughts about priests being able to marry. I think for SOME priests that marry, it may help the church. For others (which I have spoken to) it will only redirect their focus and not give the attention needed to the church. There is countless of pro and con arguments that are fair and understadable. In the end, it appeared to me that it depended on the priest. Some would do just fine being married and others it would be best they shouldnt be married. From my understading most priest would not rather not marry. At some point the Church decided that it would be best for the priest to not marry to better serve the Church. That is their bride.
What I think is odd is all these polls are asking catholics what they want but they don’t bother asking the priest what they want.