It'd certainly be possible to make this work well enough for a lot of us.

Yes, you'd need to sort out pricing. I'm unusually price insensitive, but too many sellers play stupid games and win stupid prizes (me shopping around instead of blindly buying from them every time) by changing unit prices too much too often (e.g. my sons preferred shower gel litre price regularly rotates between prices that adds up to a factor of 3 difference, with any given size container at any given time potentially being a massive rip-off). You could fix that by letting users configure price bands and make it pick from a set of products based on price parameters or give an error. Or only include products where the sellers agree to not play stupid games.

But now your UI is massively complicated and you have error scenarios you didn't have before.

Even then, though, the bigger problem is that there just aren't enough product categories where we frequently order the same thing often enough separately from e.g. the weekly grocery run, to be worth it.

In my household I think it basically boils down to shower gels - because I have a teenage son - toilet rolls, dishwasher tablets and washing machine tabs.

That's not nothing, but it's not going to make me order materially more from Amazon to be able to press a button to reorder vs. pull out my phone, press "orders" in the Amazon app, and find the last order I made and reorder the product.

And I say this as someone who did order a couple of Dash buttons when they came out and promptly forgot to even use them (and I don't even remember why).

It's just such a very minor convenience that to work it'd need to have absolutely zero friction, and even then the revenue it'd bring would likely be totally marginal.