Eventually you'd have a ruling class of people who were engineers, doctors, professional soldiers, etc. working together to maintain order over a lower class of people who need their skills.

In that case, you'd want to apprentice yourself out to the doctor. Offer to be his assistant in exchange for learning how to fix people. After awhile you'd get good enough at digging out bullets and curing staph infections that you could rise to a position of rank and no longer have to work because you'd have an assistant doing all your dirty work.

tl;dr a government of skilled workers and professionals doesn't sound that bad.

I don't think it would bring back feudalism, moore like good old fashioned tribalism mixed with maybe a little bit of ethno tribalistic tendencies we see in today's street gangs

Oh my God Jenga I can't read that post that image keeps making me laugh

The intial reaction would be tribalism of some sort, but as things stabilize and population growth occurs, the power dynamics would change. Once the basic question of survival is answered, politics will enter the picture as those with more meaningful skills will begin to be able to assert political weight against those with less meaningful skills. Farming, while important, will not be seen as valuable as healing. Organization will become necessary, thus leaders will emerge in one fashion or another. This could lead to feudalism since tribalism doesn't seem capable of scaling to the level of townships or nation-states.