I'm not convinced that the problems were connected to his leaving, and it was just coincidence that they began around the same time. You might remember that he posted on Instagram about his departure, saying that he was tired of his kids growing up without their father at breakfast in the morning. You will also recall that he had three other "meal tickets" on his plate ... he was host of The Voice, co-anchor of Today, and also doing Last Call. Even Ryan Seacrest hasn't tried to do that much all at once.
CBS was already starting to phase out the "Amp" brand and 97.1 was the very last to drop it ... and that didn't come until 2015, by which time it was not CBS but Audacy. So it is my opinion that being the last station using a brand that was created under different ownership and management contributed more to the situation than anything else.
If anything, Carson Daly picked a good time to exit. I think the switch to the "Now!" brand under Audacy would have happened anyway, and I don't see anything that would cause me to think they wouldn't have shown him the door at that point.
Just my opinion, but thank you for asking.