I take issue with Lycoming icing being very rare, having experienced it.
1977 Cessna 172N, Lycoming O-320-H2AD. Nice summer day, nearly 70 deg, going up for solo pattern practice during primary training. Marine layer has just cleared and lots of aircraft are queueing up for departure. Do a run-up, then lean and pull to 900 RPM waiting for takeoff sequence. It takes a while. On takeoff, apply full power, full rich (of course), and the aircraft climbs nearly normally (but in retrospect, it was a little weak considering I was solo -- but would have been normal for a larger load). At 400 AGL, the ice breaks clear and the engine ingests it, stumbling. Thinking I lost a mag, I push the nose down intending to set it down in the bayside mudflat, and the aircraft accelerates level. OK, still flying, so I turn crosswind and complete the pattern. Once on the ground, I give it a mag check on the parallel, and it's totally fine. Since it isn't explained at that point, I abort the practice and park the airplane.
Maybe that wasn't carb ice, but conditions for it were absolutely perfect, and symptoms completely consistent.