Isn't that the point of the block reward? To incentivize the miners to secure the network until such a time that transaction fees will be enough?

A bitcoiner only needs the security provided by miners while a transaction is being added to a block. After that, its in the blockchain and secured by nodes... Not miners. So if anything, running validating nodes provides the security for hodlrs...

What's the incentive for running a node?

- Being able to privately inspect and verify the block chain

So when I drive my car down the toll road, I pay the toll. When I park my car in the parking lot, I can park it for free somewhere and hope their security and privacy is good, or I can park it in my own garage I maintain and keep it secure and private on my own.

I don't need to pay to maintain a road I'm not driving on directly. I do pay indirectly because of inflation, as block rewards are mined my share in the network shrinks relative to the whole. This is the price I pay until there's enough drivers to upkeep the road.