Michael,
I am looking at the old-line MOR stations and not the ones that would eventually be called "AC" which, when they began appearing were often called Chicken Rock because of exactly what you stated regarding currents without the hard stuff. I'm looking at the point up to the earliest 70's, while what you describe matured from that point on.
An example I lived in the early 70's was the WAPI vs. WERC adult battle in Birmingham. WERC was current, with lots of recent gold and hit rotations that were close to those of the Top 40 competitor. WAPI, more traditionally, had the crooners, occasional big band songs or more recent "modernized" remakes, and a more limited group of currents, none of which overlapped WSGN, the Top 40 station.
WAPI had "Hello, neighbor" local announcers who talked a lot and (at least to me) said nothing. But they were warm and friendly and the did the transitions to news and weather and other features well. WERC was the flagship station for the Crimson Tide (Roll, y'all!), a morning guy who also did the Alabama play by play and a big newsroom. But, prior to becoming WERC it had been WBRC, an old-line MOR Taft station (WKRC, WGR, WTVN, etc.) which played music perhaps even older than WAPI. WERC won. Almost instantly.
Taft, like Westinghouse and several other owners of traditional MOR stations, sort of wobbled around trying to be definitely adult but not old fuddy-duddy. I remember WKYC (or whatever the calls were in 1969) editing the "other half" of "Aquarius / Let the Sunshine In". I was friends with their sales manager then, and he gave a distinct demographic / advertiser spin to that incidents and mentioned that they wanted to be very careful so as not to be compared to NormBob's wild WIXY. That sensitivity was, in part, due to a failure to launch Top 40 period about a decade before when they were trying to go up against WERE and WHK.
The Birmingham radio war was repeated all over the country in some form. WJW and WGAR are two pretty good larger market examples, with WGAR going towards a gold based AC and WJW staying in the tradition of Big Wilson in mornings, complete with his piano in the studio and bits and pieces of Stardust and other standards. As I was programming that format, I watched what was happening elsewhere and I'd say that the death of most traditional MOR presentations ended in the early 70's and truly in a roughly 5 year window.
Sure, there were MOR-ish stations like WGN and WIND battling it out, but they were gradually changing the music while they held on to the Wally Phillips and Howard Miller image of "Adult radio with no kid's stuff". (Interestingly, when I did diary reviews for WIND in the late 90's, we'd see "Howard Miller WIND" written in. I believe Howard departed to WGN in about 1968.)
I think it's important to note that there was a transition by at least one station in every market to a more contemporary music list by a station that had been the home of Doris Day and the Rat Pack. In many cases I looked at back then, the transition was often delayed because management and sales were worried about the "loyal listeners" and the reaction of clients who, themselves, listened.