It secures the network by validating consensus rules for your own sake and for the sake of everyone connected to you. If node runners were to drop their nodes, they’d lose their voice in consensus and nodes following different consensus rules (that might power multiple different wallets) could force their own agendas.

The whole point of Bitcoin is to be able to have regular people audit the chain. If more hashrate is given to a chain that can make Bitcoin at-will, none of the people they’d transact with would respect their proposed balance. So in a way running a node secures the network by having someone you transact with notify you if you’ve drifted from the consensus rules and vice-versa.