I find my 2-stoke stuff, even with stabilizer, tends to put up a fit after sitting for 6 months. Once it's going in the spring though it's fine for the rest of the season.
I'll keep using stabilizer, the $12 I spend a year on the 1L bottle isn't hurting me, and I've never had a problem with any of my stuff starting up after long sleeps. The Camaro, for example, had gas from 2016 when I put it back on the road this summer....I could smell the gas was a little off, but the stabilizer kept it good enough that I burn it through rather than pumping it out. Even modern stuff like the Sonoma....I only burnt half a tank in it this season, so when I stored it last weekend I topped it up with no-ethanol 91 and put some more stabilizer in it.