When you say the "barrier to entry is so absurdly low" you seem to mean that you could start a competing web site yourself for almost no money. And you could... but how will anyone find out you exist, and once they do, how will you convince them to buy from your site? Amazon has buying power, reputation, selection, and cheap fast delivery. They didn't get there overnight, and neither can you.
It's true that the other big names are not taking it lying down. More and more are offering shipping subscriptions, for example. But it's not so easy to convince someone to pay for multiple reduced shipping services from other sites once they have paid for Prime. You're right that there's little risk of actual monopoly though.