Whether or not one has the third Confiteor before Holy Communion in the Extraordinary Form of the Mass is a subject that can raise hackles all round.
What is forgotten, though I have mentioned it before, is the fact that the very reception of Communion during Mass is a comparatively recent custom. I don't mean because people formerly didn't go to Communion very often —when I was a child, my parents would go three or four times a year — but that it didn't happen at Mass, and Communion at Mass didn't become commonplace until the years after the First World War. At Westminster Cathedral, Communion was distributed between Masses in the Blessed Sacrament Chapel. Here in the seminary at Wonersh, Communion was distributed before the early morning 'Community Mass' until about 1925. Thanksgiving was made during the Mass itself, at which, often hymns were sung. There was a later High Mass in addition, and the entire college were expected to assist at both but communicate at neither.
The rite of Communion had a Confiteor because it rarely took place at Mass, but was a separate rite simply lifted in. Given the success of the movement for frequent Communion and the Liturgical Movement's achievement in moving Communion habitually to within Mass, it made sense to ask whether that Confiteor was necessary, if the Communion were to be treated as a part of Mass itself.
There are a number of things that have changed as a result of moving Communion to within Mass. I suppose few people now would think it inappropriate (indeed it seems an obvious thing to do), but there is no question that it has shifted the focus of the celebration away from the Sacrifice and towards the people to some extent. One encounters increasingly the attitude that if one has not received Holy Communion, one has not been to Mass. Some go as far as to assert that if one has not received Communion under both kinds, one has not received properly, and therefore has not really been to Mass. This does need some corrective action, though perhaps returning Communion to an extra-Missal position might be going rather far.