In the US, out of the four major carriers, only one (T-Mobile) offers post-paid service that is cheaper if you bring your own device. For all the others, the monthly price is not affected by if you take a subsidized phone or not. This makes it advantageous to constantly "upgrade" your phone when the contract is up. Doing so does lock you into a contract with high early termination fees, discouraging you from leaving. The only advantage of being month-to-month with those carriers is if you are planning to switch. Also, given the fragmentation in spectrum usage in the US, switching carriers usually requires purchasing a compatible phone.
The MVNOs such as Virgin Mobile, Boost Mobile, TracFone/Straight Talk/Net10, and others operate a little differently and may offer lower prices if you bring your own unlocked device.
For pre-paid service, you usually have to pay for the phone up-front, so there is often no subsidized price.
I understand that the situation is different outside the US, so it might very well be cheaper in other countries to pay the full retail price of the device.