I'd like to offer a theory of mine that could perhaps answer the question. But as far as classic hits stations that do a good job in balancing genres, I'd have to give the nod to CBS Radio. They are not cookie-cutter. WOGL in Philly tends to lean Motown, Soul etc. giving them a more rhythmic lean. WOCL in Orlando has a number of programming elements to it that reflect a rising Hispanic community, such as their dance-themed shows etc. But at the same time, they occasionally go way back to the early 60's but still their overall sound is nothing like your parents oldies station.
If you think about someone who is 40 today, they were born in 1972. If you figure by time they became at least 10 or even early teens, their music radio listening would have been on FM not AM. FM was a different animal. Because FM had so many more music formats than AM ever did, it saw the beginning of getting away from a mass-appeal approach to a target audience approach. But even in the 70's, I noticed AM hit music stations almost always power-played the very biggest hits no matter what. Here's an example. Who can forget "You Light Up My Life" that seemed to be #1 forever. AM had no trouble over-playing the song. At least on FM I remember at the time, the rotation clock was slowed way down. After all, FM was trying to convey a "cool" image and Debbie Boone just didn't fit in no matter how well the song sold. Again, on FM it was all about specific target demos.
For people growing up, let's say in the 80's, CHR on FM wasn't as mass-appeal as it once was on AM. There were also rock formats that were getting lots of attention too. Listeners were also exposed to AC at work, let's say, and artists such as Elton John, Fleetwood Mac, Billy Joel etc. Even though many of those songs were now 10 years old, these listeners would continue to be exposed to them for a considerable amount of time. It probably explains why classic hits formats, especially when they morphed from traditional oldies power-played those artists. Add the Eagles too, how could I forget that overplayed band?
Indeed, there was a lot more to music in the 70's and 80's than in what we hear today on the radio, but I think it all boils down to what is the most familiar to the most number of people who are in the 36-49 age range. I'd love a classic hits station to embrace more of the music I grew up with, particularly 70's music that actually went beyond the core artists I mentioned above. But then, radio is not targeting listeners like me who were listening to AM music radio in its' heyday of the mid 60's to the mid 70's. Still, there are some bright spots. CBS radio, for example, offer music specials such as A-Z or Top 1000 countdowns etc. Many of these songs are featured in those occasions. So, all in all, it's a pretty good trade off.
Here's a specific song that can probably explain it all and I mentioned this before in one of the other boards. I grew up in the NYC area and listened to WABC most of the time. "Sweet Home Alabama" was not a song that made it to WABC. Either it didn't sell well enough in the NYC area or it didn't fit the criteria of the station. I didn't become aware of that song for at least 20 years after it came out. Today, Classic Hits WCBS-FM regularly features that song. Also, whenever they do listener requested countdowns, that song lands near the top of the charts. I left NYC in the late 70s and moved to Florida. But apparently, a new generation of listeners were exposed to that song on FM. As time has gone on, I've noticed CBS-FM move further away from sounding old WABC like to more of what WHTZ was like decades ago.
As far as classic hits and what they offer in 60's music, I think that too goes back to what FM hit music stations were doing in the early 80's. I can't speak for all CHR formats but in South Florida Y-100 every once in a while would feature a 60's song after their morning news. The feature went something like that's the news for March 28, 1982 and then the jock would shout March 28, 1968 and play a song popular then. But what is interesting to note is many of those 60's songs I remember hearing on Y-100 back then have still survived today. AC back then featured a number of those songs too and I suspect it gives some familiarity. Then the oldies formats took off and there is familiarity among even more 60's songs for people who weren't even born yet.
But in the end, it's all a numbers game. Feature too many 60's and early 70's songs and a throwback to those glory AM days and you risk being out of the money demo. But even after all of this, classic hits formats tend to be too restrictive. CBS-Radio is still a good bet though as time goes on to feature the soundtrack to many across multiple decades.
Thanks for bringing this subject up - it's a good one!