If bitcoin somehow managed to create a system in which general CPUs were the only thing that can be used to mine, it would just mean that we'd have CPU shortages as the people with wealth and power would buy them all up. Or at least, they'd buy up all the best ones and the plebs would get the low clock speed units that can only hash at a fraction of the rate.
The "one CPU, one vote" idea sounds nice to those of us with democratic ideals believing all humans should have an equal vote, but it just fundamentally doesn't work in practice.
Any form of computing power, whether CPU-based or GPU-based or ASIC-based or memory-based, is a possession that can be accumulated by the wealthy in order to grant themselves power.
Mining is not (and cannot be) a perfectly private thing that the wealthy and powerful have full control over. Ultimately, they operate at the pleasure of governments. They are subject to political whims. A nation state could theoretically nationalize all miners in the country if the political capital to do so existed.
What makes bitcoin unique to fiat currencies, is that it is democratic on a global scale between organizations and entities that control energy production and the technological capacity to produce efficient computation. And how these organizations use their voting power is still ultimately driven by the politics within, whether that's democratic or otherwise. It's not "one person, one vote", it's "one hash, one vote". The distribution of voting power across the globe is a constantly evolving thing that depends on how much electricity and computational efficiency different localities can muster.
This is why I personally think bitcoin will be the next global reserve currency. It automatically gives proportional voting power to countries based on how effectively they can summon computation, rather than how effectively they can summon violence and destruction.
Monero has implemented just such a system already (the RandomX PoW algorithm).
By the way, bitcoin miners do not vote. It's not a democracy. Proof of work is not voting. That's important. Democracy would be a terrible system for governing money. Bitcoin is not a democracy. (Some of the proof of stake coins are, and that's bad.)
And why should CPUs get the vote?