But you are absolutely wrong about rivalrousness. A server providing readable data is infinitely renewable

Not infinitely, no. Only up to the point where usage of the server reaches capacity to provide an acceptable quality of service, and even before that point, performance will degrade with more users, though perhaps imperceptibly at first. Being able to sequentually renew (i.e. not "use up") is not enough as you can see from the wikipedia page on rival goods

A hammer is a durable rival good. One person's use of the hammer presents a significant barrier to others who desire to use that hammer at the same time. However, the first user does not "use up" the hammer, meaning that some rival goods can still be shared through time:

Again, I'm not talking about the information. The information itself is unquestionably a public good. A particular server (such as those proposed to paid for by this proposals) is not a public good. It has rivalrous physical resources such as processing power and bandwidth, and people compete to use those resources.

The reason that roads have historically been considered to be a quasi-public good is that it has been (and is still largely) impractical to infeasible to restrict access to most roads, making them effectively unexcludable. You aren't going to put up a toll booth on every corner, and if you try doing it on some and not others (apart from specific chokepoints such as bridges are certain limited access highways), the traffic will just move around it, making the scheme again impractical. This is somewhat becoming less the case technologically (due to automated toll transponders, automatic license plate recognition, GPS, etc.) and we are indeed starting to see more methods of exclusion such as express lanes, urban congestion zones, usage-metered registration fees, etc., making them even less of a public (or more precisely nonexcludable) good.

Anyway, back to servers. It is very practical to restrict access to servers with API keys. As I said earlier, I would support an SPS proposal to pay for servers which are restricted to limited-capacity use for developers and perhaps other categories of cost-sensitive users where there is a clear strategic reason to do so. I think that is a better use of limited resources than subsidizing profitable businesses (which experience has shown are highly prone to use free servers if they are available), opening the general floodgates, and discouraging (via a carrot, at least) people who can easily do so from running their own nodes (which leads to at least unnecessary centralization and fragility).