You can run a private node perfectly fine and be part of that distributed permissionless network.
Public nodes are run for incentives. if that incentive will not exist, the whole LN will be a failure.
Discussion
Totally agree but incentives are different for everyone, not just routing fees and not always monetary even. For builders with small projects it's normal to run a lightning node that is, at least temporarily, not profitable and many times not well optimized
You can do that (building apps on LN) in many ways:
- run a private node connected to a good LSP / public node
- run a public node with 4-5 good channels only, with good peers, as a decoy for a private LN node dedicated to your project
Nobody says that first you have to be profitable as LN node in order to build your project. But you have to take in consideration why somebody else would open a channel with your public node.
For example, I see Rizful (disposable) nodes perfectly fine for a small project. With just 1 or max 2 channels, well positioned, it is more than enough to have some liquidity for building a project. You can run both public and private channels on it.