But why would anyone then pay you to develop that app? They would need a business model of their own that doesn't rely on selling it, or maybe some other form of locked-down ecosystem where it is physically difficult to reproduce it even if it were legal to do so.

If the app is just a way into some other paid-for service, that could work OK. It would be similar to businesses contributing to OSS that is available at no charge today because they build related services that they do charge for. But this sort of model only works for a subset of the valuable apps produced today.

So, like websites? A surprising number of the apps I’ve worked on had websites with similar features.

Don’t get me wrong, some things may be well suited to the current model: a hiking GPS needs good maps, good maps are expensive to make, that expense is currently recovered with copyright licenses… but even then the best maps seem to be from the government, e.g. Ordinance Survey in the UK, and that app development could easily be nationalised and funded from taxation the way all NASA’s output is.