Yes, I think overall, you are not wrong. Monetary incentives are used to keep the system intact. And this works pretty well in a lot of cases. But in most, if not all of those cases, the reason it works is because what makes monetary incentives work is the fact, that they are used to secure monetary value. Meaning, if you screw with the system, you lose the money you've put into.
This becomes a whole different story if you introduce non-monetary elements into the mix, because they can't be easily measured. For example, you write the proof of existence of a contract between two parties into the blockchain. This is information is pretty much worthless for everyone except the involved parties. And what if for one party, the existence, or rather non-existence of this proof of existence is so valuable, that they are willing to dump millions of $$$ into destroying it?
Monetary incentives only go so far. For some, $10,000 is a huge sum of money, for others, it is pocket change. Securing a global network based on something like this alone will work most of the time if all there is to gain is making others lose money, too. But as I tried to point out above, once you get other information in the mix, you might get yourself in trouble, because the alignments aren't so clear anymore.
This itself might be reason enough to separate pure value based Blockchains such as Bitcoin and concepts like smart contracts, blockchain as a service and so on.
Now, back to the question, what can we take as a security instead of money? What I am thinking of is basically showing goodwill: you secure the network for a certain amount of time and in exchange, you earn the right to make a transaction (or rather a interaction). As I wrote before, things will be more complicated than that, but that is the main idea: You securing the network earns you the right to use it.