Supporting the network is meaningless concept. Miners get paid a lot of money to be online and do the Proof-of-work. This is the most important concept in Bitcoin.
Its just that very few understand the actual incentive mechanism and there is a lot misinformation, even by the most prominent core developers. Whether you run a node or not, for the outcome of the network it doesn't matter. Bitcoin is Proof-of-work, and unless you're running a big mining operation it doesn't matter what you do. Mining oligarchs on the other hand can participate in the politics (to an extent which is not clear).
#Full nodes matter, because they decide which transaction reach the miners and which not, they are also the interfaces to the network for light wallets. You cant have only 10 full nodes for the miners and call it bitcoin.