I finally figured out why. The problem is simple: those tiny windows (they're only a foot or so tall) made it impossible to see out the passenger side, and difficult to see out anything else. I maintain a mental map of what's around me as I drive, and that was difficult at best.
The H3 is basically a dressed-up Chevrolet TrailBlazer, and I was surprised to discover it's not a lot more money (the Luxury package version I had as a rental has an MSRP of just under $33K). Even so, I doubt I'll be getting one: even though pissing off enviro-wackos is a desirable feature, I buy a vehicle to satisfy myself first and foremost, and this one does not.
(I'd have included a link to the H3 page, but the entire Hummer site is one big Flash page. Why?!)