I've only ever heard employers complaining about the worker's compensation, not employees. Your perspective is a unique one.
In any event, you don't have the option of not being covered by worker's compensation laws. Your circumstance would automatically be covered by the law simply due to the fact that you were injured at work.
Your signing or not signing anything is irrelevant. When you sign, you're only acknowledging that you received whatever paper they're giving you. If you tried to pursue a case outside of what the worker's compensation law allows for, a judge would toss it out automatically.
ADD: Why does anybody insist that anything is signed at any employer? It's paper compliance and bureaucracy. If you were to actually READ those forms, as I have countless times, you would see that they simply inform you of your rights and obligations under the workers' comp act, but at no point do they actually ask if you would like to participate. If you were to refuse to sign, as some employees do, your employer would simply mark "employee refused to sign" and it would ultimately change nothing.