Nothing massively wrong with SS on the road, I’ve had a couple of SS road bikes though have only used them for shorter rides – the 30 mile commute and up to 80 or so miles. The steeper climbs aren’t as bad as you think once you get the knack of wrenching them up, though they’ll kill you at first. Where it gets frustrating is in gently rolling areas, where it’s daftly inefficient to spin on the shallower descents but equally there isn’t enough gradient to make freewheeling worthwhile. With gears you can just keep the power on. Gears are faster, there’s absolutely no question about that, but then speed isn’t always the only thing.
IMO there is a benefit over gears when it comes to foul weather commuting – the SS is just maintenance free if you have a decent (WI) freewheel whereas gear cables do start to stick and a geared drivetrain does start to suffer slightly when it inevitably gunges up.
Fixed vs SS, I can’t get on with fixed myself. Too scary at high speed, and if you mostly ride freewheels and forget you’re on a fixed when you need to come to a quick stop you can be in proper trouble. I speak from close-shave experience. YMMV.
I confess I’ve moved the SS road bikes on and my winter bike now has gears, but if I was commuting by bike more than once a week through winter I’d almost certainly have an SS.