whenever you think of a change or a new feature, etc. you should mainly think about the dishonest people not the honest ones. in this case rewarding full nodes means any dishonest person can start up hundreds of nodes with very little effort and cost to get all that reward for himself.
now you have to think of a way to prevent this type of fraud. it can only be prevented to some extent and only with a hard fork to change the mining algorithm.
now you are left with a new algorithm that has other flaws in it making it less safe ergo making bitcoin insecure.
and the issues keep on piling on, and for what? to pay people to run full nodes? there are already thousands of them doing it for free.