Running a node that does not mine produces no revenue and no blocks. What it produces is independent verification, and that is the function the network's guarantees actually rest on.
Verification and production are separate roles
Miners assemble blocks and compete to have them accepted. Nodes check whether those blocks follow the rules.
A block violating any rule is rejected by every node that checks, no matter how much work went into producing it.
Miners can choose what to include and what to build on. They cannot make invalid blocks valid, because acceptance is decided by the machines verifying them.
Your node enforces the rules for you
A wallet that queries someone else's node accepts that operator's answers about balances and confirmations.
A wallet backed by its own node checks every block itself, so it will not accept a payment that violates the rules regardless of what anyone reports.
This is the meaning of not needing to trust a third party. The guarantee is not that the system is honest; it is that you checked.
Distribution is what makes rule changes hard
Because each node enforces its own copy of the rules, a change requires operators to adopt new software individually.
Widely distributed nodes make coordinated change slow and highly visible, which is precisely the property that protects properties like the supply cap.
Concentrating verification among a few large operators would leave the written rules unchanged while making them far easier to alter in practice.
Privacy improves as a side effect
Querying a third-party server reveals which addresses you are interested in, which is enough to build a picture of your holdings over time.
A local node downloads all blocks and filters them itself, so no external party learns which transactions matter to you.
Broadcasting from your own node also avoids revealing to a service which transactions originate with you, which is a separate leak from the balance query.
The cost is modest and mostly one-off
The initial synchronisation is the demanding part, requiring the full history to be downloaded and verified once.
Afterwards the ongoing load is small, since keeping up means processing a modest amount of data per block on hardware that does not need to be powerful.
Pruning options discard old blocks after verifying them, which cuts storage substantially while preserving the property that the operator verified the chain themselves.