So there's pretty much nobody that can catch up to this level of dominance, not even the second place players. Which is a clear sign that Amazon should be broken up by the government.
Even if the software is well implemented, there's still issues of items being damaged during the pick/pack step, items being labeled incorrectly, put into the wrong bin, misplaced, or even stolen. These are things that smaller shared-warehouse store fronts don't have the capacity (in space or money) to cope with it.
For some European countries there's PriceSpy that scrapes prices and shipping costs (I suppose it scrapes as I would guess e-commerce entities would not publically expose API to query their products). It works OK most of the times, but sometimes it reports old or not updates prices, so I would say it's not foolproof.
We got a free ShopRunner subscription through Amex and I was excited about that but they seem to be mostly for clothing.
But the biggest annoyance is that we no longer go straight to Amazon to buy something, we actually have to shop around, google for things, etc. And Google Shopping isn't as useful as it used to be. A good shopping aggregator would go a long way in helping.
Edit: We were frequent users of the shipping, by the way, and never used streaming. Unlike others that use mostly streaming and not shipping.