This particular hill is not one most libertarians would choose to die on, but I will make a few points:

First, monopoly city trash collection does have a long and dishonorable history in some places of corruption, organized crime, and mutual company/government backscratching. Just saying.

Second, is the current system less expensive, offering better services to the residents? Are they paying individually? Who would get the "savings" they're talking about? A good point has been made, which is that once a monopoly has been put in place, choices go away, and you are at the mercy of the monopoly. I've never lived anywhere that had more than one trash company servicing it, and it didn't kill me, but my fees have steadily increased and the garbagemen have gotten to be prima donnas about many things. I do know that my TV service improved drastically when we finally got a choice of more than one way to deliver TV signals to my house. How did those old cable monopolies work for everyone else here?

(As an aside, it's fascinating how horrified liberals are at the idea of private monopolies, giving many reasons how they abuse customers, but government monopolies are just dandy.)

Third, any product or service at all would be more "efficient" if restricted to a single monopoly provider. Assuming of course efficiency is the highest goal. Think of all the waste generated by having hundreds of brands of cereal.