There is a downside to designing a mining algorithm tuned for general purpose CPUs: anyone with access to a lot of general purpose CPUs (such as botnet operator

There is a downside to designing a mining algorithm tuned for general purpose CPUs: anyone with access to a lot of general purpose CPUs (such as botnet operators, or government groups) can easily aim their existing resources to try to do 51% attacks against the cryptocurrency. If the mining algorithm requires specialized hardware, then no group starts out with an existing advantage. If the NSA decided it wanted to 51% attack a cryptocurrency, they'd have to make a massive investment in their own hardware, and then that hardware can't be repurposed after the attack. A 51% attack is likely to devastate the value of a cryptocurrency, which also de-values any mining hardware built for it, which naturally discourages anyone who invested in mining hardware from attacking the cryptocurrency. Though mining algorithms that require specialized hardware also come with their own downsides: the companies that invest in making the mining hardware early on could decide to keep the most advanced mining hardware for themselves and gain a lot of control over the network.