If everyone called everyone priest that you might have something like this. But this is not the case. Your priests are professionals and do most of the ministering. They are the only ones known as priests and they are probably the only ones that are allowed to perform your various sacrements. I think there are seven sacrements and there may be cases where a non priest can perform them.
Baptism, Confession, Eucharist, Confirmation, Marriage, Holy Orders, Extreme Unction.
A layman, even a non-Christian can perform Baptism as an emergency when the baptised is about to die. The valid trinitarian formula must be used, as well as, of course, water, and the celebrant must intend that to be Christian baptism. I am not aware of other exceptions.