Awardless blockchains

Ok, this may be the stupidest idea I've ever had; this may be the stupidest idea anyone has ever had, but I'm gonna put it out there anyway, if not to discuss it's viability, then at least to entertain you with my stupidity.
It is also possible, if not probable, that this idea has been discussed before. If that's the case, I apologize.

Anyway, here it is:

This idea is not meant to be some kind of value transfer., like most coins are. If anything, it is related to those crypto 2.0 ideas like ETH, Lisk, Factom and so on. The closest use cases I see at the moment are Proof of Existence and maybe Proof of Ownership like cases.

All blockchains I've seen so far are built on the premise, that you have to reward those who maintain them, be it PoW, PoS or some variety of those, either by transaction fees or by generating new coins.

But what if there is a blockchain, that does not generate rewards for those who maintain it? The first thought would be, that nobody would maintain it, which is a valid assumption. However, there can be "outside" and non-monetary incentives to maintain it.

You could obviously create a donation system to pay those who maintain it. This could keep the "miners" (I'll call them that for now, although this is obviously not the right term) from trying to game the system. If implemented in a sensible way, it would also prevent the arms race, PoW mining has become.

But I'd like to look at it from a more philosophical, if not idealistic point of view. The cryptocurrency community seems to be built on a philosophy of distrust, that the only way to get people to contribute to a system is to let them earn rewards, which in cryptoland means to earn money (or at least let them think they earn money). While I understand this way of thought from a rational standpoint, I don't really like the idea from a philosophical point of view.

There are projects out there, that are inherently altruistic, or if not that, based on non-monetary rewards, be it reputation, honing your skills or knowledge in certain fields, or other things. Freeware comes to mind, or Wikipedia (although Wikipedia may well be one of the more "donation-based" kind). This makes me think, that a blockchain, that doesn't rely on tokens of any kind, could actually work, if it's use case attracts the right crowd of people.

A problem such a blockchain has, is obviously the risk of senders spamming the network. How to prevent this, I am not sure, but one possible solution could be to make them solve similar functions as miners have to (which might, interestingly enough, lead to not mining, but sending pools).

Ok, you may now laugh at me and this idea, either by yourself, of by commenting on it.

Forgive my weird wording and incomprehensibility, it's late over here and I need to go to bed.

Regards