I've never been a 3000' rule believer, but I still thought it was fun to update my list with those I'd met the 3K.
Here are my interpretations for how to credit your hike with 3K status:
1) You must have been 3000' below the summit at some point on your hike. Example: I climbed Bierstadt from Guanella Pass, then traversed the Sawtooth to Evans and back to Guanella Pass. No credit for 3K, since I was never 3000' below the summit of either Bierstadt or Evans, evan though I did gain over 3000' counting the ups and downs.
2) If you meet the 3000' condition for mutiple peaks on your hike, you can choose which one you want to assign the 3K. Example: I climbed Grays and Torreys from Stevens Gulch. I could assign the 3K to either Grays or Torreys. Later, I climbed only Grays from Stevens Gulch. So, I can credit the first 3K to Torreys and the second to Grays.
3) To count multiple 3K peaks on the same hike, you would have to drop 3000' below the 2nd after summitting the first. Example: I climbed Belford, Oxford and Missouri on the same hike, with ~7500' gained. I can see the argument that 2 peaks could be given 3K status, but choose to only credit myself with one, since I didn't drop to 3000' below the summit before ascending either the 2nd or 3rd peak.
Anyway, this is my version of the 3K rule. I'm not actively pursuing it, and I'm a believer that if you summit all the 14ers you 've legitimately completed the list regardless. However, I will probably have fun picking up a new 3K summit from time to time, and maybe I'll even be a 3K completer eventually.
Regarding lower peaks, I think you could track it, but most folks pursuing a lot of 13ers, 12ers, etc would rather go somewhere new than return to the same area to re-climb 2, 3, 4+ 13ers just to qualify. John Kirk at some point had a goal to do 3K for the centennials, but I think he gave it up as he broadened his peakbagging goals.