Lots of states don't require it. Know your state's vehicle code and how it applies to bicycles. NY state law specifically states you're not required to carry a driver's license to ride a bike. Cops can't "make trouble" for you if you're not violating a law. They can try, but it won't stick and people who know their rights and the laws will have no issues generally. If they start "making trouble," you just politely ask them to write you a ticket for the rule you're breaking. Then you'd go in front of a judge and it would all be tossed out. Cops can just write tickets. It's courts that decide what does and doesn't stick.

That doesn't mean I condone people riding like morons on bikes or anything like that. I think they should be held to the same standards as motor vehicles as it pertains to traffic law enforcement.