Its a social problem and all it takes is one player breaking through. People have done this with far far worse things that people thought were unviable socially. Microbetting, microloans, gaming microtransactions, hardware subscriptions,
Sites like the internet archive are already funded by donations from viewers like you. I see the scheme as essentially spreading out the donations based on who uses the most bandwidth. It makes it easier for anyone to spin up a mirror of archive.org, and it makes it more secure for sites like archive.org to accept donations.
"Intermediate" micropayment solutions already exist. Anna's archive charges like $5 a month for a "donation" that puts you in a fast lane to download PDFs that you would otherwise have to get from some book site or a scientific journal. I bet they would prefer to charge per-download if they could feasibly do it.
I agree that some (most?) applications of micropayments are really gimmicky. But some applications are naturally suited to micropayments. The advantage of micropayments is that you can interact with ad-hoc vendors without setting up a pre-existing financial trust-relationship. For example, you could be at an bus terminal and have several pop-up vendors for wifi or electricity that charge per MB or per watt-hour. It enables competition.
The more gimmicky applications you mention like hardware subscriptions all involve some element of vendor-lock in that prohibits the advantage of micropayments systems in dealing with ad-hoc vendors. This is more analogous to those in-flight wifi services on airplanes: there is an established financial relationship with the airline and no competition, so there's little use for the low-risk micropayments.
Internet archive is not funded on donations from viewers. Its funded off government grants and corporate donations. individual donations make up a tiny %. Micropayments would make Internet archive less reliant on charity from government and corporations and it would not impact peoples ability to spin up a mirror. people can already spin up a mirror but its expensive and would remain expensive.
Anna's archive is whale pricing, a tiny % of people are willing to pay that $5 and the hope is that they subsize costs for the rest of users. I hate this type of monetization and will always oppose it as its highly risky and unfair.