If the second Misreatur vestri and Indulgentian absolutionem (as well as the second Confiteor) were removed from the 1962 missal, ...
Happy & Holy New Year. Puer natus es...
Objectively speaking, communion of the faithful is NOT part of the mass. A priest can celebrate mass alone (normally though with a servant) and it is completely legit and valid, of course. You don't need any faithful present for the Trad mass. It is the unbloody Sacrifice offered to God by the priest.
My old 'Missel Quotidien St Joseph' missal (Copyright 1962) has a clear demarcation for what is the : "Communion of the Faithful". The French rubric says: 'If communion is not distributed, we pass over the part in red Brackets'. see attached photo.

But then you get these modernists who insist that the mass is basically a meal, "Supper", people of God, community blah blah... The New Mass is, I suppose, really awkward if no one is present. So the N.Ordo ommision reflects this bigtime: They removed the second Confiteor because now communion has become an integral part of their NEW LITURGY.
In days gone by, with the strict fast from water or food from midnight, it was a practice to give communion very early Sunday mornings, so, outside of mass, as Lads alluded to. My parents told me this. After that communion, people would go have breakfast at the relatives...some would have fainted otherwise, esp expecting mothers...
In my opinion, the removal of the Second Confiteor is a creeping modernist decision.
I also remember Fr. Paul Aulagnier, R.I.P.+ ( the first one to contact +L waaay back), told us in Suresnes that he was travelling with 3 others in a car (de Mallerais etc. ) and they were discussing if the second Confiteor should be kept or not - as they were driving!!! He said: "THE FUTURE of the Mass is in this car!" He ended with a big laugh, as usual.
SSPX has always kept it - now you know!!