I commuted on a singlespeed almost daily for over 10 years. Similar length commute to yours (16-18 miles depending on the route I took) but about half the elevation and nothing steeper than about 5%. That enabled me to run a fairly high gear which worked well for maintaining decent speed on the flats and descents without having to grind too much on the hills.
I loved that bike, the simplicity of it was just great for commuting, very little maintenance and very few mechanicals. And definitely made me a stronger rider who was comfortable and smooth at a range of cadence. Would thoroughly recommend it if you can cope ok with the extra climbing on your route. I did also try going fixed gear but just didn’t like it at all, even on the modest descents I was doing I didn’t feel it was safe to be still having to pedal while also dealing with traffic, pedestrians and other hazards at speeds >30mph.