Earlier quoted context omitted.
Those are all problems with a specific, objectively crappy container, as you've noted. There are many alternative containers and no reason the podcasting community couldn't come up with its own, such as by extending Matroska. This obviously creates separate problems, but I'd like to see the podcasting community start to shape its own destiny a bit rather than expect others to innovate for them or kludge older formats…
One of the OP's requirements is that this work in iTunes, which precludes making a new container format. I also think existing containers would meet the requirements - for example, Ogg meets the requirement of both being storable and easily streamable. Also, the Matroska spec is being updated to a new version, and being standardized in the IETF CELLAR working group. I'd highly suggest participating if you'd like to h…
Matroska draft: https://datatracker.ietf.org/doc/draft-lhomme-cellar-matrosk...