Another possibility is that Bush took a tip from his father and intentionally chose a Vice President who he knew most people would find unthinkable as President. A little insurance against impeachment.
I think that was Nixon’s plan too but Agnew screwed it up by getting caught for his own crimes.
I’m a bit curious as to why the OP’s questions comes up now, several years after all that.
Anyway, several posts have already suggested that Cheney chose himself to be the VP; and perhaps that he meant to all along, and never had any intention of choosing anyone else; and that his VP-search was just a charade all along.
That’s exactly what I’ve always believed, but I’ve suspected one thing more: That Cheney and Bush had a deal, right from the start. And (without any real evidence) I’ll even suggest a more cynical deal I suspect they had: I think Cheney said to W: Let me choose myself as your VP, and I’ll let you be Prez.
So maybe the OP’s question really should have been: What would the Country, the World, and Everything be like today if Cheney had chosen somebody other than W to be his President?
(Confession: With respect to the W administration, you can see that my cynicism transcends all rational boundaries.)
I was prompted, actually, by the recent article in the Times, which got me wondering who else Bush had considered for a VP. Not much info on that, as it turns out, but I then started wondering What If.
I suspect that if Bush had pick McCain* that it would have been a great improvement. He was far more honest, less evil and more fiscally conservative then Cheney. He probably would not have pushed W and the world into the war against Iraq. He would not have pushed for the authorized use of torture. Of course he probably would have been far weaker a VP then Cheney. So who knows if it would have really made that much of a difference. The Puppet master would probably have still pulled many of the same strings.
** (old tradition of taking the #2 from the primary, much as Reagan took on Bush the Elder.)*
Cheney would have been a competent president had the need arisen. I would have violently disagreed with about 95% of everything he did or said, but that doesn’t mean he couldn’t have done the job in a professional and efficient manner. I mean, it’s not like he’s Sarah Palin.