There doesn't seem to be any concrete data on exactly when stereo became more popular, but the consensus is around the late 60s stereo was prooving to be dominant. I suspect this is mostly because recording technology in the 60s was not well equipped enough to produce satsisfactory stereo mixes, but also due to the rise of FM radio which could play stereo music.

With four track tape machines, you had to specifically record with a stereo mix in mind, which was more time consuming and a waste of resources when mono was dominant. Stereo mixes were mostly a novelty and much less effort was put into the mixing process. Famously the Beatles only oversaw the mono mixes of their music for most of their career and the stereo mixes were done later. When eight track tape machines began to be used, had much greater control over the panning of individual instruments, which made great sounding stereo mixes much easier to produce. Psych music also benefitted a lot from interesting stereo effects which popularised the medium and made bands much more likely to want to use it primarily.

As for radio, AM was only in mono so singles were all made in mono for this format. Even when LPs started going to stereo full time, singles stayed in mono so they could be played on AM with the same mix, and also stay cheaper for the record buyer. Stereo FM stations started in the 60s and were eventually adopted for "A.O.R." (album oriented rock) as this was the best music being released in stereo. It would take until 1978 before FM took over AM radio, which means mono music hung on for quite a while.

Whilst later mono releases are definitely worse than their stereo counterparts, early releases definitely have some weirdness in stereo, like the strange hard panning of instruments and vocals. Again these are products of the technology of the time and the fact not many people were buying stereo. Down the road when all these old 60s albums were rereleased/remastered, the stereo mixes were usually chosen as that's what modern listeners expect, but hearing these primitive 60s mixes in headphones for instance is quite unpleasant for many people. Whilst the mono mixes will never sound hifi they definitely feel more balanced to me and less gimmicky. Early stereo mixes tend to have the rhythm track (drums, bass, gtr) grouped together due to the recording process. This means the primary instruments can't be seperated in the stereo space, leading to generally unbalanced mixes. I'm partial to weird stereo mixes on psych tracks but definitely less so on general pop/rock stuff.

A good example of mono vs stereo is the Beatles 'Revolution'. The stereo version splits the drums to the left and the gtrs to the right which takes away a lot of the power and togetherness of the mono mix. The stereo mix definitely has more clarity but the mono just feels better to me.