Spoiler (and question)
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"the people may never join in with the "Through Him, with Him, in Him..." prayer"
Or, . . . . . . . what?
They go to hell. Duh. ;-)
Seriously, it is an illicit practice, which means it is against the rules of the Church. And since we believe Jesus told us to listen to the Church to willfully and knowingly disobey would be a sin.
On this particular point, the idea is that the priest and the people serve two different functions. Some parts of the Mass are for the priest to say, some for the people and some together. This blurs the distinction between priest and laymen. It is the priest here offering the sacrifice on behalf of the people assembled.