This would require everyone to understand that previous certs still require high-security for at least a few weeks post expiration. This is not something we can rely on people understanding.
Alternatively we could have people understand all certificates, regardless of expiration, are high security. Is there any reason someone would want to publicize an expired certificate? Additionally, I can think of a few existing reasons someone would avoid publicizing an expired certificate.
I'm pretty sure that most people, upon having one of their certs expire, do not find the private key and release it publicly. In fact they often generate a new cert from the same key...
Allowing bypass is the old way of doing things, and many non-browsers still allow it, so you should ideally hold on to old certs indefinitely, but at least for a short while.
I think this is reasonable for people dealing with SSL, like expecting a mechanic to know you change an oil filter when you change the oil.