I honestly don’t know if I’ve read/heard this idea before, however, I’ll put it out there for people to critique…
Using NIV Matt 6:9-13.
Given that the audience is the disciples, “Our” probably wouldn’t be considered all inclusive, although I guess some might argue that? “Father” is quite powerful, as is shows the loving relationship of God to people, in particular His people (whoever they might be). Again how broad this is would be debatable.
Google confirms that this means “Honor as holy”. This is where I think it really starts to get interesting; The only way for God’s name to be truly “hallowed” is for people to become Christians.
If I take one of my favourite kingdom passages, Dan 2:34-35, that could mean UR
God’s will is done perfectly and universally in heaven, therefore we are praying for this on earth, and again the only way that’s possible is if everyone was a Christian!
God is provider and cares for his Creation, in particular Christians but there is what some people call “Common Grace” (please correct me if I’m wrong about this).
There might be something here but I can’t see it yet.
Again not sure if anything directly related to UR.
Furthermore, as I’m an optimistic post-millennialist, I see this prayer as asking for something that will actually happen.