Probably depends on the manufacturer. Subaru and Nissan seem to come up all the time with various problems over the years, while Honda seems to have theirs fairly well sorted. Granted, newer models have probably been updated and work better.
Several of the Toyota hybrid CVT's are not what you would consider a 'normal' belt CVT but something very much different and are very stout, same goes with the Ford hybrid versions (Toyota and Ford cross-licensed some tech many years ago). No belts in these and really not much to break.
But.....I'm with most car people that don't like the driving experience. Even my wife, who could not give a flip about driving doesn't like her dad's HRV with the CVT. I would tolerate one in a daily grocery getter I bought for fuel milage though, but I'd have to have something else to drive for fun.