One big problem with the CVT as used on scooters is that it has nowhere near the gear range as a manual transmission. It is severely lacking on the low end. This becomes very obvious on my 125cc scooters. They run out of gear pretty quick trying to climb hills. The lowest ratio available on the CVT is nowhere near low enough for most hills. OTOH, my Genuine Stella with a manual transmission will literally crawl up a steep grade in first gear, barely moving but keeping the engine in the powerband. This prevents engine lugging, bogging, and eventual engine damage due to putting to much of a load on an engine in to high a gear. The big scooters have enough power that they can get away with a limited gear range. But a true automatic transmission, like in most cars, is the real answer. Either that or a CVT with dual range, like the old Honda trail bikes. Some way to get a much lower gear when you need one. I would prefer an actual automatic transmission with a torque converter.
2002 Vulcan 750 (now being slowly reassembled) 2013 Royal Enfield B5
2001 XT225, 2009 Genuine Stella
2012 Zuma 125, 1980 Puch moped