This is a weird view, albeit a common one among die hard free market lovers (I've even heard the "dominant in their niches" thing verbatim, although I doubt folks could expand on what that means).
The typical individual outside of our profession is not choosing a browser because of a feeling of entitlement. They have maybe 5 hours of free time in their day outside of work / commuting / kids / etc. I doubt they have any idea beyond "this browser works, is fast" or heck "it's installed" as a reason to choose their browser, especially if it's a mobile browser.
Free markets do not solve the issues of monopolies. You don't even have to look to history or the current market to understand that. Monopolies are an unfortunate natural tendency that the market heads towards when uninhibited, because they afford the maximum amount of profit. It also, at least until the monopoly hits a certain point, affords the max amount of efficiency and quality to the consumer.
Unfortunately, by the time the monopoly takes over, there remains no real "choice" left for the consumer to run to. At that point, the profit maximization takes over completely and quality begins to drop. After all, the incentive is just to be better than the "others" who remain, who likely have almost no resources (and moreover the monopoly probably introduces proprietary standards to make remaining alternatives worse).
At that point, we get stagnation, which I would argue the world has seen a good chunk of in recent years. Price fixing, collusion, all too common among the top (see the recent controversy with Google and Facebook working together). Why fight for the "free market" as you call it, when we can work together to rest comfortably?