I imagine that the micropayments system would be facilitated transparently through some popup in the browser, similar to how the browser asks for use of your webcam. I also imagine that some basic, configurable limits would be involved. It would look like "Give news.com ability to request up to 0.10 cents (0.01cents per page load)? Y/N". The first time you load the page.
This is an aside, but in an ideal world, such a mechanism would also be used to reduce fingerprinting! You would have to accept a popup for a page to use features like WebGL, for example.
>Any legitimate financial tool needs a way to roll back fraudulent transactions.
I strongly disagree. I would even say the opposite: the ability to bureaucratically roll-back transactions threatens the legitimacy of money. Specifically, it makes the money non-fungible.
In cryptocurrency, there are transparent multisignature-based escrow systems that allow you to have a defined window of time where the money is co-managed according to certain rules. But transactions need to be able reach a "finalized" state where they are irreversible. Otherwise you just can't ever have a truly secure method of payment between untrustworthy parties and micropayments become useless.
Also, it does not need to be cryptocurrency. Micropayments just need to be efficient, secure, and irreversible. There are other payment systems based on Chaumian cash, (GNU taler being one example) that this could be built on.