That's pretty much what a monopoly is, and even in your niche, not everyone wants to be a monopoly.
I have a friend who runs a small craft beer bar. Another craft beer bar is going to open two doors down. To him this is great - the area becomes known for craft beer and more people come along. There is no monopoly there.
>> For example, Microsoft has a monopoly (in this case a government one) on producing Microsoft Windows, but Microsoft Windows is not the only PC operating system.
But they tried to make it that way, and came close for a while. That's the time period they had various anti-competition lawsuits aimed at them.
This is what most people are talking about when they are talking about monopolies, and it's clear that not every business aims to be one.
pbhjpbhj's comment implies that by addressing a niche market, you would avoid the drive to monopolize. I'm arguing that if you are addressing a niche market, you are working to monopolize that market, and you don't have to monopolize the whole market of similar services to be a monopoly. For example, Microsoft has a monopoly (in this case a government one) on producing Microsoft Windows, but Microsoft Windows is not the only PC operating system.
Similarly, you could monopolize a certain demographic. For example, Microsoft has an effective monopoly in PC operating systems when it comes to government administration workstations in most countries.