"If this is so, isn't it almost probability 1 that CEV will be abandoned at some point?"

Phil, if a CEV makes choices *for reasons* why would you expect it to have a significant chance of reversing that decision without any new evidence or reasons, and for this chance to be independent across periods? I can be free to cut off my hand with an axe, even if the chance that I'll do it is very low, since I have reasons not to.