Yes, Cardinal is not a divinely-instituted position, but it’s bad form nonetheless because of what Cardinal originally is.
A Cardinal, in its most primitive form, was simply a cleric (priest or deacon) “incardinated” in one of the parishes within the Diocese of Rome, and shortly thereafter, in the surrounding suburbicarian sees. So from the beginning, Cardinals have always been tied to the clerical state. When you became, say, a parish priest or a permanently assigned parish deacon in the Diocese of Rome, you were a Cardinal.
This is also why to this day, anyone named to the College always receives a titular church in Rome. It’s also the basis of the three degrees of Cardinal: Cardinal-Bishop, Cardinal-Priest, and Cardinal-Deacon. Back in the day, they were really bishops, priests, and deacons of Rome (and area; the Diocese of Rome, of course, has only one Bishop).
It’s also why Cardinals are named Cardinals of the Holy Roman Church, not the Holy Catholic Church. Because again, they are still, at least in title, clerics of the Diocese of Rome.
Women cannot be clerics, and calling a woman a Cardinal carries implications that have no basis in history and open cans of worms that really should be left alone. It implies or at least carries the optics that the woman is in the clerical state, and that is not possible.