"Sole provider of a service" is perfectly compatible with a free market. It happens all the time where there are niche or narrowly focused small markets, where there is not enough potential profit for multiple providers to exist long-term.
"Monopolies" can only exist through force, usually government force.
Example: I grew up in rural Arkansas, when Wal-Mart was just a regional chain retailer starting to spread its wings. Wal-Mart numbers their stores in the order they opened; they currently have ~8,500 stores, but up through college (graduated 1985) I never shopped in a Wal-Mart with a three-digit store number.
Even back then, people screamed about "Wal-Mart is killing the local mom-and-pop stores! Wal-Mart is killing local pharmacies!"
Truth? Local stores that don't try to compete, but instead offer added value or unique merchandise, actually do very well when Wal-Mart comes to town. People naturally miss that local touch, and are willing to pay more for personal service, and sometimes they just want to wear clothes that obviously didn't come from Wal-Mart, like everyone else is wearing.
This is in a highly regulated market, not a free market. Why would you expect an actual free market to provide less diversity?
Oh, and let me point out that the threat of competition is just as real as actual competition: in the late 1970s to early 1980s, when Wal-Mart first got into the pharmacy business, we heard tales of woe about how the Waltons would kill local pharmacists by undercutting their prices, then raising prices as soon as the local pharmacies closed.
Funny thing about retail pharmacy: it's a highly competitive business. As soon as one pharmacy closed because of "Wal-Mart's predatory pricing", another popped up, so that Wal-Mart couldn't "jack up their prices", as had been predicted. Wherever local clothiers were "run out of business by Wal-Mart", others either modified and thrived, or popped up to fill the demand for clothing that wasn't cheap crap from Indonesia.
Why would private security be any different absent a state monopoly? Especially when you consider that Wal-Mart fails to be a monopoly with government assistance?