They can. See https://blendle.com/, though the going rate there is considerably more than 0.01. But that's a question of pricing, not of logistics. The way it works is that you pay a small-ish lump sum up front and then you draw down that balance in small increments. That is different from true micropayments where you can send small amounts to anyone on demand, but it's a proven model.
The real problem is that to scale this beyond payments to a fixed set of vendors you basically need a license from the federal government. You need to either be a bank or a money-transfer agent, and both of those have extremely high barriers to entry, basically insurmountable, mainly to prevent money laundering, which is the tough nut that no one has been able to crack.