Not if the company providing the competing browser goes out of business and stops offering it.
That's really what antitrust regulation is for: to prevent one dominant company from killing all their competitors. Once that happens, the dominant company has no more pressure to succeed and their product stagnates, harming everyone.
Browsers are actually a great example of this; despite the government prosecution, Microsoft succeeded in killing off Netscape and then had the entire browser market to themselves. The result was IE6 and "made for Internet Explorer", a horrible mess that took years to clean up.
But it’s not really how the world works though as bigger companies use this soft power for everything, which is why I have stocks in FANG and it just keeps going up and up.
It’s a bit like Atlassian, no one is happy with Jira by itself but they do have the whole package.