The sad thing is... we do. 24 hours is a bit much, but why not have a different certificate for each server? The whole point of a certificate chain is to give us the flexibility to issue and revoke certificates from lower down in the tree... of course most of us serfs don't get the privilege of using our own intermediates.
Oh... and we're repeating some of the same mistakes in DNSSEC. Looking at deploying DNSSEC I kept reading that the general idea of the KSK was to function as a long-term key, and the ZSK as a short term key, but I have yet to see a method of managing things with the KSK offline that isn't like pulling teeth. The latest BIND requires that both the KSK and ZSK private keys be resident on your primary nameserver when you switch on the "auto-dnssec" magic.
Still, at least setting up DNSSEC is free.