Concelebration is an ancient and venerable usage of the Western Church. But the culture of concelebration as we now have it is not. 'Traditional' concelebration is an expression of the unity of a presbyterium with its Bishop and, mediately, of each presbyter with each of his brethren who is also a member of the presbyterium of that bishop. It is particularly associated with Sacraments and sacramental rites; and it is not confined to the Eucharist. Presbyters join with their bishop in ordaining by the laying-on of hands in the ordination of a new member of the presbyterium: thereby being able with their bishop to do something which they could not validly do on their own.
Likewise, they concelebrate the Consecration of the Chrism; before the Council, indeed, representative presbyters, fully vested, joined the Pontiff in the insufflation. Dom Gregory Dix wrote in 1936: "Though the bishop alone recites the prayers over the oils, these priests are real 'concelebrants' with him ...This 'concelebration' is one of several points in which the consecration of the Chrism has retained elements of the most primitive Christian liturgical practice which the consecration of the Eucharist has now lost".
Sadly, the newer rites have reduced the Traditional Concelebration of the Consecration of the Chrism to the mere gesture of the Presbyterium extending its hands during part of the ancient prayer. But this is something ... and better than nothing.
My view is that presbyters among us should look forward each year to concelebrating the Chrism Mass, and the consecration of the Chrism itself, with their bishops in Holy Week, and to doing so with joy, rather than tut-tutting in corners with precious like-minded chums about how this sort of thing really is something that we elite cognoscenti now know better about. (Not that I am convinced about this renewing-vows rigmarole ...)
And after all, Maundy Thursday is a day when we are not allowed to say private Masses.
But I certainly agree that very many of the concelebrations that take place nowadays, particularly where there is no bishop presiding qua president of a presbyterium, are indecorous and unnecessary. Traditionalists, in my view, should not be making (unsustainable) attacks on proper concelebrations, but developing a healthy new praxis. At the heart of it there should be the assumption that each priest should say Mass daily, either with his people or 'privately'. There should be a restoration of the experience of seeing a whole lot of priests in choir, not because they're too lazy to have said Mass on their own and can't be bothered to concelebrate, or think concelebration is a 'status-conscious' thing, but because each of them has carefully and devoutly said his own Mass previously.
These are not the views - and this is not the praxis - which have been mine throughout my ministry. I believe that at this time of retracing interrupted continuities it is right for us all to reconsider questions which, perhaps, we once considered closed. And to do so on sound grounds - not just on the principle that pendula swing. I hope I am still learning and still rediscovering.