There is nothing that is non-Catholic about your Uncle’s point. In fact Jesus makes the same points leading up to the Lord’s prayer that we should not repeat words for their own sake, and also that our Father knows what is in our hearts before we pray and that we should pray in private.
So you should encourage your Uncle and support his assertions.
Meanwhile, we also know that Jesus did give us this prayer and that for many of us, the prayer is easy to remember, and since we know it contains Jesus’ wisdom, we want to get it right so that we can contemplate it each time we say it. So we don’t HAVE to use it as a template and try to make up our own, we can use it directly.
I have heard it said by one of our priests who used to be a Baptist, that Catholicism includes everything that the Baptists have.There is nothing that is Baptist that isn’t also Catholic. But, Catholicism has some additionally things - or the fullness of the faith. Try to remember that when you talk to your Uncle. He should find it comforting that everything that he believes is Catholic.