Independent of the merits of Bush's foreign policy objectives, it seems to me to have been instrumentally irrational to be such a consistently bad friend to America's friends; it's made the attainment of those objectives harder, and may have soured important relationships in the medium term.
....Has there been any underlying rationality to the administration's shabby treatment of Blair?
1) The administration thinks it has made concessions to Blair. In 2003, Bush did not want to go back to the Security Council a second time to get support for the use of force in Iraq. It did so precisely because Blair needed this step to bolster his domestic situation.
The result was that the U.S. looked like it was undercutting the U.N. more than it acually wanted to (no mean feat in 2003). I'm sure senior Bush officials blame Blair for the fallout.
2) Washington is tone-deaf to compliant states. Readers, raise your hands if you've heard of the NatWest Three. My guess is very few virtual hands went up. In the U.S., the extradition treaty at the heart of this case is a non-issue, while in the U.K. it was front-page news for much of July.
I suspect the administration would have preferred ratifying the treaty. I also suspect that since there was no domestic political gain from pushing the issue, and Great Britain was not going to shift its foreign policy because of this issue, that preference does not translate into anything.
This also explains Bush's attitude in his recorded conversation with Blair from St.Petersburg as well. At the time, there was a lot of blog commentary about how Bush's foreign policy nostrums were crude and simplistic. Watching the tape, my reaction was rather different -- Bush seemed like someone who was way too comfortable being the most powerful man in the room. Clinton would have been glad-handing everyone there to make them feel welcome. Bush, besides an odd backrub, acted like he expected a line supplicants to come along and offer flattery and foot massages. This arrogance of power is precisely the kind of behavior that annoys populaces in other countries.
3) It's the "grim trigger" strategy of diplomacy. Particularly after 9/11, the Bush team adopted a particular diplomatic style that I've labelled the "diplomacy of the grim trigger" in a chapter I've written for an edited volume on the transatlantic relationship. Shorter version -- a diplomatic approach that might wring concessions from potential adversaries is way too brittle to apply to allies.
I'm sure there are other possible explanations. Readers, have at it!!