Happily, And with your spirit will now be heard in RC churches. I imagine there will be churches, particularly in America, where congregations which have been corrupted by unfaithful priests into disrespect for Tradition and the Magisterium, will ostentatiously continue to use And also with you. The reason for the change - if they bother to listen to it - will probably be even more offensive to them than the change itself. Spirit refers to the spirit impressed upon the soul of the ordained minister at his ordination whereby he is distinguished from the laos. The priest (or, before the Gospel, deacon) invokes the Lord upon the people and they respond by praying for him as he prepares to discharge the leitourgeia which was committed to him in priesthood (or diaconate).
In the EF, this exchange ocurrs more frequently; it precedes pretty well every significant recommencement after breaks or chant. Sadly, it has lost this significant role in the OF, being prescribed only before Gospel, Eucharistic Prayer, and Dismissal. This makes it all the more important to use it at the start of Mass, despite the unfortunate provision of alternatives. Surely there is no more important moment at which Priest and People should remind themselves and each other of their different but complementary taxeis in the liturgical community.