This is a granted monopoly. It has real positives, such as the same service at 5x less road wear. It should also be obvious that to be positive overall the deal needs to prevent abuse of the public.
They are given 5-year contracts, but an agency exists to tabulate complaints, reaction time to outages, and so on. If they don't impress the agency near the end of their contract, it will be opened up for market bidding.
Because of this pressure, the monopoly power company has even been known to reduce rates, proving a priori that they are indeed serving the public interest at a commendable level.
If there are 5x as many truck runs, the trash per truck is 1/5th.
The more likely result is that each of the providers runs far fewer trucks than a single provider would because trucks and drivers cost money. Unless the 5 companies figure out how to get the total revenue to 5x, they can't pay for that.
Let's do an example.
Suppose we have a street with 100 houses and it takes 5 houses to fill a truck. Therefore, it will take 20 truck runs to collect that street's trash.
If there is only one trash company, it will need 20 truck runs to service that street.
If there are five trash companies, each with an equal share of those 100 houses, each of those companies needs only 4 runs to service its 20 houses. Why would any of them do more runs?
Yes, the average distance per run may be higher for the 5 companies, but it won't be 5x.
You contradict yourself at the end of the comment. Yes, it could be estimated a linear equation (mx + b) where m is the cost per house and b is the cost per route, roughly. And then you could have a system of which equations, where each row in the system’s matrix corresponds to an additional company.
The optimal result is probably not 1 company, but it’s probably not 1 company per house either