What I mean is, something similar to what these guys are doing in Foldincoin, Gridcoin, etc:
https://www.foldingcoin.net/https://gridcoin.us/http://www.trnicely.net/dense/dense1.htmlThere are many critics of Bitcoin that argue how "Bitcoin's PoW wastes too much energy". I can easily refute that by pointing to how it secures your bitcoins being safe. However, what if we also had hashes being solved that were relevant in other contexts (see examples provided). We could make multiple points of the hashrate usage.
Did satoshi avoid this in purpose to avoid possible game theoretical incentive problems so he made it strict bitcoin without side use cases?
Bitcoin's PoW is easy to reason about, which makes it easier to analyze it from game-theoretic point of view. "Useful" calculations add a big amount of complexity and often require some sort of centralization. This makes them unsuitable for being used in consensus algorithms for big networks like Bitcoin, where security requirements are very tight.
This question is very common, so you can find a lot of information about it if you do some digging: