ok, i was pointing out plenty of artist do both. Any band with one guitarist usually plays both. I was watching this band saturday night and i noticed one guitarist was using an ebow and being very careful with his volume, so he was basically, from a lead/rhythm standpoint doing neither. He became like a different instrument. I saw the rhythm player playing slide on this old peavey that looked like a univox but sounded great. He was no longer playing rhythm, he was now lead. That's when it hit me. The keyboard player was the rhythm. The violin was lead, and the guitarist traded lead licks and went back and forth in different songs playing both but the keyboard player was the glue. It was a lightbulb moment, like ding. Me and my wife were analyzing it and when we figured that out it came together. The bass player and the drummer were locked in with normally the left hand of the keyboard player. He was doing variations of the melody with his right hand or just keeping everyone together. The reason the guitarists could do what they wanted was because that guy was the rock. He mattered. He was mvp. He walked away towards the end of this 15 minute jam and we were just saying how great they were and when he went grab a beer it was obvious something was wrong. The one guitarist sounded out of tune. The keyboardist was turning the oscillator thing and he was keeping the one guy (he was playing a les paul and he sucked) from sounding like crap. It started to come full circle. He was shifting the pitch slightly with the keyboard because they were off and he was important. The minute he stopped you knew how important he was.
My answer is rhythm. The rhythm section keeps you from sounding unorganized and all over the place. There must be some order even in the middle of chaos.
I have pics of his keyboard, he was making music on it, that's for sure.