While I am unsure if switchting to Linux for ME is a good solution, open sourcing whatever runs ME is a very important step towards user/customer security. And that is not because we all want to know intels secrets about 'how to make the fastest CPU' but because ME can change the product on a fundamental level while we use the product.
The reason I doubt that Linux is a good solution is that linux wasn't built to run somewhere deep inside a cpu with very little overhead. Surely, it can run nearly everywhere, I just doubt that it is the best choice for that job.
Just to be clear: I love Linux, not just for what it is, but also for what it does and use it every day since more than a decade.
A shrunk version of Linux can run on 8088 CPUs too.
https://github.com/jbruchon/elks
But the problem here isn't to put this or that OS in place of Minix but rather to get rid of that completely for good. Different licensing also wouldn't help at all: behind those people are the ones who actually write the laws; it would require 10 minutes of their time to make an exception for terrorism or child porn motivated surveillance.