Is it possible to use something besides sheer computational power as the limiting factor on block release? Why hasn’t anyone tried to create a blockchain that, rather than using computational capacity as the hash scarcity test, just has a direct limit on how many times a particular wallet can make a guess per day? (or something like that..)

I’m just thinking that the whole arms race for processing power means that the system isn’t really as democratic as it initially seems. Like sure, you don’t have a fed that controls inflation, but every new crypto currency from now on will be mostly owned by whoever has the most ASIC farms won’t it?
direct limit on how many times a particular wallet can make a guess per day? (or something like that..)


Guess per day for what?

You can't limit it by wallet since you can't know what addresses are in a wallet. To the network, there is no such thing as a wallet (and technically no such things as addresses or Bitcoin objects either). If you were to limit it on a per address basis, then people would just generate infinite addresses (because they are essentially infinite and you cannot prevent people from generating as much as they want) to do their "one guess per day".


  but every new crypto currency from now on will be mostly owned by whoever has the most ASIC farms won’t it?


No, that is completely incorrect. Miners are not an absolute authority and do not have a final say on anything. The consensus rules are something that everyone who uses a coin follows. If any consensus rule is violated by a block or transaction, that block or transaction will be rejected by everyone who is validating consensus rules, i.e. the full nodes. So no, miners don't control it or own the currency because they cannot force changes onto the community and it would be pointless to mine a coin if you are the only holder of it (i.e. there is no market so no value).