In theory, cryptocurrency can probably do this. Even as someone who is extremely critical of cryptocurrency and blockchains, this is actually one of the few use cases in which it makes sense - "Hey Bob, I want to buy a business license online. If I give you a $20, can you give me some bitdollars?"
On the other hand, this probably won't work out in practice. Cryptocurrency exchanges do fall under KYC, so the documentation burden still exists. The unbanked could build their own exchange... if they had the capital. In addition, the high level of technical complexity and the need to trust in the unseen (proof of work stakes aren't as good as physical bills when it comes to trust) means the benefits are negated compared to just using the grey market to have someone transact on your behalf (which is a common practice for the unbanked, and also my uncle who still doesn't understand Amazon).
Someone could solve these problems, but they'd need to maintain an ongoing company to do so, which would again trigger KYC and downstream fees.