He's got something there, I suppose. Only if you believe in the absolute sovereignty of God and his ability to override our human mulishness would such prayers make sense -- and yet we all offer them.
On the other hand, I replied at the time, "Yeah, well, did you ever notice that when we pray for the illnesses of our friends and ourselves, we all pray like functional Arminians? We all say, 'Lord, heal me/them,' and we try to get all our friends to pray, too -- as if God took our wishes, and the multitude of the wishes of others, into account. But that's only possible if God is an Arminian God."
Of course, all this really proves is that we can be whatever we think we need to be, without our worrying over whether we're being consistent in our ideas of God. If we were honest, we'd admit that what we need is for God to be whatever he needs to be, without his worrying over whether he's being consistent with our ideas of him.
Prayer for those without Christ
For all those whose hearts are restless
because they do not rest in you,
For all the lost sheep straying on the hillside,
For all the rebels who would rather rule in hell
than serve in heaven:
Have mercy, Lord;
Speak to them in such a way
that they might finally hear, and come seeking
your rest, your fold, your peace. Amen.
-- AWC, My Lord Knows the Way Through the Wilderness