"we" do a checkout /shakedown dive anytime we have new bits AND as the first dive of every vacation diver trip. "they" ask us to perform a checkout dive for the first dive of every vacation trip. These mostly match, they do not always align, but no real issues. We are on vacation. Relax!
All of the vacation dive ops we use stress that the first dive is a checkout dive. This does not mean the dive site is crap, in general it is as good as any other site we see all week. The "checkout" reminder seems to be more of a mental flag to pay attention (which you should always be doing). But they only seem to stress weights. No basic kneel on the bottom skills demo (thank you!). This attitude makes sense as lots of divers seem to require some weight tuning (different wetsuit, more bioprene, forgot my weight from last trip a year ago,...)
I now believe that competent dive ops treat the check out dive as an informal test of diver competency. On a recent trip we had a certified rescue diver panic in 35 feet of clear caribbean water on the checkout dive.
I treat the first dive of every trip as a checkout dive and always leave the camera behind. If we have a new piece of gear we try to not employ it until a few dives in, if possible.
A few years ago my divebuddy purchased a new prescription mask. She used her old mask for the first day and we planned a specific dive on the second day to test out the new mask. We did a buddy pair shore dive and I left my camera behind. This dive was to test out the new mask (strange bifocal mess) to make sure it was comfortable, did not leak and allowed her to see things. Pre-dive we discussed what issues may cause an abort - leaking was yes, uncomfortable was a no and i can't see squat was a maybe...)
P.S. IMHO a checkout dive had nothing to do with the other thread...