Being a Cardinal implies no particular sacerdotal role beyond that which he otherwise has by reason of ordination. Even electing the Pope is not a role associated with orders, per se. The role of a Cardinal today is: 1) to advise the Pope, 3) to do what the Pope asks in the administration of the Church and 3) to elect the Pope. None of those things requires someone be ordained. Certainly it is not pointless to advise, work and elect.
Historically, the Cardinals were the bishops or neighboring dioceses, and priests and deacons of Roman churches. As such they have historically been in orders. Only since John XXIII have all Cardinals been required to be bishops - unless dispensed, e,g, Cardinal Dulles. Only since the late 19th century or early 20th has the requirement been that Cardinals be priests. Indeed, Cardinal Mazarin, who was Louis XIV’s first minister for so long, was only a deacon.
Really, there is no dogmatic reason not to have women participate in a papal election. Before the Bull restricting election of the Pope to the Cardinals, when the Pope was acclaimed by the people of Rome presumably some women were involved in that action. Certain monarchs had an historic right of veto in Papal elections - presumably that would have extended to queens/empresses regnant, even if not ever exercised by a queen. Unlike being capable of receiving Holy Orders, merely participating in electing a Pope is not limited by sex.
I don’t think we will see women electors, but there is no reason beyond tradition (small case), prudence and canon law to bar women as a group.
