This is more like a landlord evicting a restaurant and then opening a copy of that restaurant in the same location
"Amazon took my idea and did the same thing at lower cost" is basically another way of saying "I wasn't adding any value but was still capturing a bunch of money on all those sales". Maybe there's an argument there that Amazon is freeloading on market research, and we should have some kind of intellectual property protection for market research, but that seems like it'd be a policy disaster. And there are lots of businesses out there already that piggyback off their competitors' market research (for instance, Burger King supposedly just locates anywhere McDonald's can operate profitably).
This isn't always the case, as many merchants have pointed it out. Sometimes (I'm sure not all the time), it's more "Amazon took my idea, and all the validation work I did in order to develop and prove it and build a market for it, and is selling it below cost in order to force everyone else out of the market"
I'm not passing judgement on whether that is okay or not; I'm pointing out that Amazon "winning marketshare" does not mean that they're doing it in a better way, or at a lower cost. Sometimes it just means that Amazon is able to spend/risk a whole lot more money than anyone else.
However during congressional testimony last week Bezos was directly asked this in relation to Echo devices. His response was that "at list price" Echo devices "are not below cost", however stated "sometimes when it’s on promotion it may be below cost, yes."
Echo devices (for example) are "on promotion" a significant amount of the time.
Hell during Prime Day last year Amazon was selling Fire tablets for like $12 (although that was widely believed to be a pricing error that was still honored).
Amazon is a public company.
> however stated "sometimes when it’s on promotion it may be below cost, yes."
Using hardware as a loss leader isn't unusual -- you get a discount on the hardware but on average they make it back on products/services that are complements of the hardware. Keurig and every printer manufacturer do this, too.