The 1984 Statement of the Jouint Commission for Theological Dialogue between the Roman Catholic Church and the Orthodox Church which included such heavyweights as John Zizioulas and Joseph Ratzinger described mention in the Canon of the bishop by virtue of communion with whom one offers Mass as "essential". This may seem a trifle overstated - after all, there are extant Eucharistic Prayers which have failed to do this; are they therefore lacking an 'essential'? - but I believe it does express the ancient notion that the Bishop is the true primary celebrant and, as S Ignatius put it a long time ago, that Eucharist is to be accounted bebaios which is celebrated by the Bishop or by one to whom he commits it.
In the Te igitur of the Roman Canon, the mention of the Bishop is not a prayer for him but an expression of the fact that the presbyteral celbrant offers qua delegate of that bishop.
Together with the mention of the Roman Bishop, the Te igitur thus gives full expression to the synchronic unities which constitute a particular Eucharist as the Eucharist of Christ's entire Catholic Church, and not a ritual activity of a local gathered and autonomous group. The presbyter is at one - ideally! - with his Bishop; the bishops of the world are at one with each other through the ministry of Peter. Ideally!