First of all, congrats on coming back. I just came to it.
What you said is somewhat right. Maybe it would help to distinguish between "liturgy" and "mass." "Mass" is, at core, the sacrifice of the cross made present. "Liturgy" is the rites in which that sacrifice is framed. The chief purpose of liturgy then (as regards the mass), is to effect the sacrifice, not to teach us to pray. The mass is not principally a didactic ceremony. Something really happens before us, whether we are physically there or not. Sure, if you learn more about the mass, what it is, and what the various parts mean, you will certainly learn more about your faith and how to pray better. But that is not its chief purpose. The sacrifice, being perpetuated in time, brings down God's grace into the world and into our souls. That is its chief purpose.
Actually the Mass is principally a didactic ceremony. The Mass and the other sacraments are the first and foremost instruments in teaching and virtue and the moral law. It is not its primary principle but a principle nonetheless.
How is it the "people's" "work?" Well, we "assist" at mass by uniting our souls to the sacrifice effected by the priest. That is our work. A validly ordained priest effects the sacrifice there at mass. That is his work. The people have nothing to do with it. But they reap the benefits of it, and they unite themselves to it, and receive the graces. It may help to realize that the priest has his part, and we have ours, and they are not the same. You don't even have to know what he's doing and saying in order to unite yourself to the sacrifice.
Just because the people don't effect consecration of the bread and wine does not mean that the people have nothing to do with it. They do and they ought to. They ought to receive our Lord and give themselves to Him as well. To do this the people ought to sing when they are meant to. This is the desire and will of the Church for the Liturgy as it is Her official Public Worship of Her God. We are members of the Church too and ought to fully participate in that worship.
I've gone to a few Novus Ordo masses since converting, and I have to say, it's maddening. They're distracting you with this and that the whole time, and they don't give you a moment to collect yourself and unite interiorly with what's going on. You come out feeling like you did the hokey pokey for an hour.
That has absolutely no bearing on the Solemn Tridentine Mass with the whole congregation chanting. The under participation that you are advocating is exactly what lead to the over participation in the liturgy and the Church today. We need to seek for the proper and active partcipation according God's Will and that is for the whole parish to sing the propers and hymns and responses according to their abilities.