Some thoughts:

First of all, Jackson Five, Delfonics, Commodores, Four Tops, Supremes, and pretty much all the great soul/R&B/Doo-wop groups had ******* boffo-ass top-tier vocal harmonies, especially when compared to OP's examples (REM and Kings of Leon SMH). The Emotions, the Coasters, you could go on from the 50s through the 70s and beyond.

Second of all, if the focus on white people is so important to you, how about the Mamas and the Papas, Crosby, Stills, Nash, and/or Young, a lot of the canonical "Southern Rock" bands, the Eagles... mostly terrible, terrible music, but great vocal harmonies (and better than ******* Kings of Leon and REM).

Third of all, Sting singing solo doesn't count as "vocal harmonies" no matter how great his range was (hint: it wasn't). Some vocalists DO accomplish great things by harmonizing with their own vocals via multi-track: Tori Amos and Björk leap to mind, there are others. Rufus Wainwright. Avant-garde mainstays like Diamanda Galas and Laurie Anderson. Weirdos like Mike Patton and Andre 3K.

Also, Frank Zappa's bands always used vocal harmony a LOT, from the early psychedelic stuff through the Ike Willis / Bobby Martin years and beyond. Note that he was heavily influenced by black Doo-wop and hated white blues.

The Roches. Can't forget the Roches.

Finally, give some of the great Wu-Tang tracks a chance -- the 1995-6 solo albums, Wu-Tang Forever, and The W -- RZA became really great at using rappers with different flows and different vocal registers, overlapping or layered, to make a modern equivalent of vocal harmony... I think he likes to think of himself as a composer but what he really is, is the best orchestrator since Duke Ellington.