I wouldn't think you'd need to create a new format, just write up a spec of what all available FOSS implementations are actually doing and agree that that's the standard going forward. Between Linux/*BSD/illumos you should be able to pretty completely describe all currently-active uses of ELF.

(Of course this assumes that doing this is sufficient to make it legally not derived from the original spec as far as copyright law cares about, which is beyond my non-lawyer ability to be that confident in.)

> Has anyone looked at creating a new object format for Linux?

No, because that's overkill for this problem, because the de facto standard is "What do modern free Unicies do", where those are basically Linux/BSD/Illumos. Besides, it's not unheard of in Unix history to have free implementations of proprietary standards, where those implementations became de facto standards anyway.

Even if it was a seriously pressing issue, writing a new specification that covers ELF as it exists today is going to be many, many, many times easier than introducing a new executable format across the ecosystem, they're not even in the same league or sport in terms of effort. If you were going to introduce a whole new object file format it would be much better to do it and justify it on the basis of fundamental technical/architectural changes.

> It's concerning that a huge open source ecosystem like Linux depends on a closed specification.

Linux is written in C, whose spec is proprietary. The larger stack has countless ISO standard references etc., all of which refer to proprietary standards you need to buy.