"Judaism long ago moved from the temple priesthood to a rabbinical model ... "

That may have had something to do with the destruction of the Temple in 70 AD, when Jewish leaders were exiled from the land, killed, or taken to Rome as slaves. In 132 AD, the remaining Jews were exiled. Judaism still hopes for the rebuilding of the Temple and the reinstitution of their Priesthood.   

"God will not be present to us sacramentally unless a priest recites certain prayers, we should by all means retain the priesthood. Let's just not call ourselves believers in Christ who promised to be with us wherever two or more gather in his name."

Instead, we could just call ourselves Catholics or Orthodox Christians - not Protestants.