The rise of the paid newsletter and the prominence of the paywall leads me to be a little less cynical about the prospect of micropayments. A decade ago, when Flattr was prominent, the culture around paying for things on the internet was very different. I was initially excited about Flattr but grew disillusioned with it, and every iteration on the idea since has, as you say, never taken off...
...but more recently, the last year or so, I have actively thought, when coming across a paywalled article, "I wish I could just pay for this article". I have subscriptions to the places I read every day, but it's a hard sell to start a new expensive subscription cold.
I am quite optimistic about the future of micropayments as an upsell strategy into paid subscriptions. Essentially, if I can pay for paywalled articles individually, and I start to consume a few per month, it'll make much more financial sense to start paying for a subscription than it would to keep going through these micropayments every time.
I agree that the "sprinkle a little money towards the sites you used in the month" remains pointless. Paying $10/month for a few pennies to go to all the different sites I've visited in the month is far less compelling than paying $1 per article for 10 articles in a month I wanted to read. I haven't used Post yet, but I am quite optimistic, I think they have a real shot at making this model work.