The issue with availability on CO vs. say AA is one of pricing. CO full F ("A" class) on EWR-LAX is $800 one-way (+tax). (Full Y is $750, FWIW). AA matches that fare with a "KUP" which books into restricted "P" inventory. When that sells out, then you're looking at $1,020 for a YUP booked into restricted "A" inventory. After that sells out, then full "F" in AA is $1,422 one-way. Maybe AA gets better yields because of the higher/more flexible (for them) fare structure. Maybe they don't; obviously the OP's experience is that there is last-minute availability because fewer people are willing to pay $1,422 for one-way F. As a result seats on AA probably go empty or to elite upgrades.

If one is a last-minute booker (or changer) then maybe CO isn't the best choice. But then again, my travel agent can waitlist me for First Class on CO, and I've never had it not clear. As an alternative, you can use ExpertFlyer to set an alert for A inventory so when there is a cancellation you can book it right away.