Actually, some Protestants do precisely what you describe — maybe not in tandem with a television or radio broadcast, but they will have “their own communion”. They do not necessarily believe (depending on the denomination) that a priest or minister has to say the prayers over the bread and wine, and unless it would be Anglicans, Lutherans, and some Methodists (this one surprised me), they do not believe that the bread and wine actually “become” the Body and Blood of Christ in any way. I am not sure if Baptists believe that an ordained minister has to preside or not.
I have wondered, in moments of useless speculation, whether, if Holy Orders were lost from the face of the earth forever — if every priest and bishop died and no man could ever again be ordained a priest until the end of time — the remaining faithful could put together a type of “agape communion”, with unconsecrated bread and wine, and say something to the effect of “we know what we have lost forever, and we grieve for it, but let us come together in unity, and as a memorial to that sacrifice that we had and no longer have”. I have in mind how the Jews have essentially “improvised” with synagogue services and sacred rites for the past 2000 years with the Temple having been destroyed and sacrifices no longer being offered. I also have in mind the unconsecrated antidoron that is given to the faithful at Eastern Christian Divine Liturgies.
Not worth dwelling on, but perhaps an interesting plot device for some apocalyptic fiction.