We get into a big gray area on "popularity", depends on where too, what part of the country. I have to say "barrel" chrome rims 10 inch wide were still pretty popular around here up into the seventies. My sister had a brand new 73ish Cheyenne with them on all four corners for a while then changed to Ansen slots. (never really liked those)
But my brother ran the chromeies up into the mid seventies and it was a pretty cool car. My truck had them put on around 72 by the previous owner and stayed their until 79 or so when I had it.
But without a doubt late 60's they were seriously getting replaced with "Mags" on cars where the guy had a few more bucks.