A single CR 15 creature is supposed to be a Deadly battle, where one or more character risk death if they sent smart, for four level 10 characters. Those characters should in theory be able to handle three battles like that successfully in an adventuring day with a Short Rest between each one.

If the party can go all out nova, CR isn't really a very good measure. I mean, it's not all that great even with it, depending on you assumptions. The measure of three Deadly difficulty battles in one adventuring day still assumes the party will survive, even if they do that repeatedly for their entire adventuring career. It also breaks down pretty fast for solos.

If you want CR = party level battles, assuming only three battles per day, to represent even some pretty insignificant chance of party defeat, you have to take into account that will eventually result in a TPK. Let's say that represented a 5% chance of TPK per battle. Over a course of 20 levels, the party might fight 120 such battles. 1-0.95^120 ~= 99.8% chance of TPK by level 20. Even with only 1% chance of TPK it's still a 70% chance of TPK by level 20. That's why the game is set up so a TPK is basically impossible under the default rules and expected CRs.