I don’t see the “plenty of exceptions?” The Lazarus “prayer” was thanksgiving.
The Priestly Prayer in John I’m not going to argue over, but it is interesting that it doesn’t really tell us what when on, and it wasn’t corporate, it was from Him alone, shown in that we don’t know what the Apostles were doing, or if He did as was His custom and stepped away.
Then how did they know what He said?
How about the parts that were addressed to them specifically, intersperced in the prayer?
OK, here’s another one. Jesus called the Temple a “house of prayer.” Did He mean that people went into little corners of the Temple to pray?
Mt 21:13 He said to them, “It is written, ‘My house shall be called a house of prayer’; but you make it a den of robbers.”
Was THIS prayer private?
Ac 1:24 And they prayed and said, “Lord, who knowest the hearts of all men, show which one of these two thou hast chosen
25 to take the place in this ministry and apostleship from which Judas turned aside, to go to his own place.”
This doesn’t SOUND like private prayer, especially considering that it is mentioned in the context of fellowship (i.e. community):
Ac 2:42 And they devoted themselves to the apostles’ teaching and fellowship, to the breaking of bread and the prayers.
Temple prayer was communal; Sts. Peter and John engaged in this form of prayer:
Ac 3:1 Now Peter and John were going up to the temple at the hour of prayer, the ninth hour.
Like I said before, at Pentecost:
Ac 4:31 And when
they had prayed, the place in which they were gathered together was shaken; and they were all filled with the Holy Spirit and spoke the word of God with boldness.
Ac 6:6 These they set before the apostles, and
they prayed and laid their hands upon them.
If St. Stephen were in private, he wouldn’t have been stoned to death!
Ac 7:59 And as they were stoning Stephen, he prayed, “Lord Jesus, receive my spirit.”
Another example of the Apostles praying communally:
Ac 12:12 When he realized this, he went to the house of Mary, the mother of John whose other name was Mark, where
many were gathered together and were praying.
I could go on and on, but I think this is sufficient.
I’ve said I do believe that communal prayer tends to be more orderly and “come off” better with rote prayers, and I don’t mean to imply a legalistic standard for others. For me, it’s private prayer.
BOTH are recommended.