Well he doesn't have that questionable career in the private sector to explain. He's certainly qualified, erudite. The relationship's a lot more traditional than the bargain he struck with W, so that means he's towing the HW line. Honestly I don't see a downside, on a personal level.
There's probably a flood of ink spilled on an administration admitting a mistake. It's yet another distraction the campaign doesn't need. But the point of Baker/Powell is to mitigate that kind of talk, and Cheney likewise fits the bill.
On the "changing horses" front, I think Quayle's drain on the ticket is overstated and this ends up doing more harm than good with undecideds and low-information voters, but it's probably taken in stride by the base.
What might be a problem- and what might have truly kept him off the list IOTL- is Mary. She's in a same-sex relationship in 1992. The follow-ons from that are massive to think about. Honestly it's probably enough that Cheney doesn't make it through the vetting process once this comes to light.