That is, there is no business activity, equity, intrinsic value
There is some "instrinsic value", but you need to know some math, to understand it. For example: Bitcoin is the biggest source of low SHA-256 hashes in the world. It also shows everyone publicly, how strong this particular hash function is. The same with ECDSA: for example, because Bitcoin exists, you can see, that 130-bit public keys and 65-bit hashed public keys are unsafe. Without Bitcoin, you wouldn't know that, so you wouldn't know, how strong your keys should be, to not be stolen by some third party.
Also note, that SHA-256 or ECDSA is not something Bitcoin-only. It is also used in other places. Which means, if SHA-256 will fail, or if ECDSA will fail, then by having Bitcoin blockchain, which is public, you have any chances to observe in advance, and predict, when it will fail. Without Bitcoin, there would be no incentive for cryptographers and mathematicians, to share their observations, because they wouldn't be rewarded properly. Think about it: maybe humans didn't solve some millenial problems, because the rewards for solutions are too small?
Another thing is also the way of claiming the reward: if you have Bitcoin, then you can solve some complex math problem, and claim the reward, without revealing your name publicly. Without Bitcoin, you would be forced to use your real name. And not everyone wants to be written in the history as "the one, who turned off the Internet, by breaking SHA-256" or "the one, who invalidated credit cards, by breaking public keys".
And they have some nonsensical limitations. The Bitcoin system, for e.g., has a limitation that the maximum sum of numbers associated with the addresses of scheme members can be 21 million.
It is easier to pick some constant limit, than to properly adjust the number of units in the system. In case of fiat currencies, how do you know, if people behind the system produce enough coins? What if they produced too much or not enough? How can you measure that? In case of constant supply, you don't have to worry about it, because you can adjust a price for a single unit, instead of adjusting the number of units in circulation.