Scale has no value unless it offers something to your customer base. What you're ignoring is that Uber, Amazon et al are so huge and dominant because customers flock to them. I can summon a taxi to my location in most cities in the world with a single app. I can have pretty much any item delivered to my door within one or two days. These were unfathomable 10-15 years ago.
Amazon has huge amounts of competition, as does Uber. I have absolutely no idea where you get this idea they are not influenced by pricing. Uber hasn't made any money in its entire existence. That is not characteristic of a monopoly.
Whether or not a functioning market economy could ever exist in reality if of course another question.
Anyway, the promise of a market economy is that it selects the "best" by competition. The fact that companies like Uber survive for decades while making losses and destroying potential competitors shows that this promise of the market economy does not stand in reality.
We don't really though. There are companies, and individuals, with enough wealth and influence to compete with entire markets. A well-funded startup can undermine whole industries by spending VC money to run at a loss long enough that the rest of the market fails (Uber, AirBNB) or they can become so massive that there's absolutely no possibility of competing (Amazon). People can start private companies that do things only governments have done before (SpaceX, Palantir). These businesses are not influenced by pricing, because they're either too well funded to care, or too influential for others to get a foot in the door.
Free market economics is a beautiful idea, but every big business (and some small businesses) do all they can to subvert the market and hold a monopoly on something. Heck, Peter Thiel literally wrote a book about how to do exactly that - Zero To One.