No, I don’t believe so. Some might, but I think many do it purely for the selfish reason of avoiding guilt etc. Just because you and I and many others see it as being good for everyone, I don’t beleive that most people think the same! They may be able to describe the act of doing something for the benefit of all, just as we are discussing, and understand it, but otherwise only want whatever they want regardless of the impact on others. Humans are selfish, all of us are, it’s an evolutionary tool for survival used by all life and helps ensure the survival of the species. Some of us regularly think beyond that though, but I reckon you’d be surprised how few do with any regulatory, it can become quite tiring to constantly assess situations afresh, so instinct kicks in and so people just do what they want in that moment that takes the least effort.
But then who are the criminals and ‘bad’ people if not those that have rejected the contract? Life is never all or nothing, so there will be times when someone will abide by the contract, for whatever reason, and times when they wont. This discussion centres on the times that they don’t and assumes that is the option taken the majority of the time.
True, a society does demand sacrifice of free will, however it can be argued that there can never be 100% free will even if you’re a hermit in a cave 100s of miles from another human. E.g. “I want to stay in my cave all day today, but I can’t because I’ve run out of food.” Hunger removes the free will for that period of time.