I agree, "What is Pop music?" is an interesting question, one perhaps without a definitive answer.
It originally referred to songs written in the classic two verses, chorus, bridge (middle 8 in England), third verse, chorus, out form. Or a close approximation of it. Also with a sing along melody and "hooky" chorus. That’s how The Beatles started out, not surprising as they based their music on the American Pop music of the 50’s and early-60’s, with some Rock ’n’ Roll thrown in. They pretty much stuck with that formula through the Rubber Soul album (with some exceptions), after which there were no more rules.
ABBA was obviously a Pop Group, but in my opinion so were The Ramones, and so are Weezer (hooks galore!). The Stones never were, nor were The Yardbirds (though in the 1960’s the British press referred to all the bands---including The Stones, The Who, even Cream---as Pop Groups. That was to differentiate between music for teenagers, and the adult music: Jazz and Classical). The Kinks are a tough call; Ray Davies wrote Pop Songs, but most of them didn’t sound Pop ("Waterloo Sunset" being one notable exception, but there are plenty of others). The line between Rock and Pop is not so clear, and as much an opinion as anything else. Is a "Pop" song performed by a Rock band Pop music, or Rock? Like Van Halen’s version of "California Girls".
When it comes to "God Only Knows", I use the term Pop in reference to the non-Pop music it shares many musical "devices" with: Classical music. It’s certainly not a Rock song, so whatta ya call it? There is a sub-genre amongst Pop music aficionados, called Baroque Pop. I suppose that’s the best we can do. That term works for Brian’s pal Van Dyke Parks too.