They wouldn't be solved because the problem is that newer versions of shared libraries are not compatible with older applications. There is no problem with ELF or PE formats - ELF is supported on Linux natively, and PE is supported using Wine.

APE format doesn't solve the problem with shared libraries changing over time, it dosn't solve the problem that different plaforms provide different APIs (for example, windowing APIs, audio APIs etc).

> APE format doesn't solve the problem with shared libraries changing over time

APE doesn't use shared libraries at all and it's intended to be statically linked?

> APE (...) dosn't solve the problem that different plaforms provide different APIs

APE provides the most important POSIX APIs (or shims) for every platform it supports.