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So Hashcash was proposed by Adam Back, who is now the CTO of blockstream, a major bitcoin development firm. His vision, and the vision you describe is actually bitcoin.

A 2017 Hashcash was actually implemented recently and published at http://hashcash.com/ Bad news is that it requires something to store the value, so this requires bitcoin as the token transferred via hashcash.

What you have described in your post doesn't actually work that way in the real world -- You cant set a global proof of work value (bitcoin difficulty adjustment) or able to build a proof of work that would allow a phone or desktop to hash -- it will be eaten alive by spam farms with ASICs (bitcoin mining asic farms).