Rotating certificates guard against bad PRNG and birthday paradox
Tbh, i have no idea which part you are attacking with the birthday attack in this specific context. It doesn't seem particularly relavent.
(At the risk of saying something stupid) - i was under the impression RSA did not use nonces, so i don't see how that is relavent for an rsa cert.
For an ecdsa cert, nonce reuse is pretty catastrophic. I fail to see how short lived certs help since the old certs don't magically disappear, they still exist and can be used in attacks even after being rotated.
But there have been several high-profile cases of bad RNGs generating multiple certs with RSA keys that had common factors. I think if you were put at risk by such a broken RNG, frequently re-generating your certs would tend to make things worse, not better.
It is extremely unlikely a modern certificate will be broken in the time horizon of a few years through a cryptography break.
All systems eventually fail, but i expect it will be several decades at the earliest before a modern certificate breaks from a crypto attack.
Keep in mind that md5 started to be warned against in 1996. It wasn't until 2012 that a malicious attack used md5's weakness. That is 16 years from warning to attack. At this stage we dont even know about any weaknesses about currently used crypto (except quantum stuff)
Rotating certificates is more about guarding against incorrectly issued and compromised certificates.