Fixie is no harder on your knees that singlespeed, you’re grinding uphill either way and you can just brake a bit if the cadence is getting a bit high on the downs. You get used to the constant pedalling in about 5 mins, and unless you have you’re saddle so, (too) high it locks your knees at the bottom of the stroke, there’s little chance of throwing yourself off.
Having said all that, coaster brakes are pretty good too. I had one on a 3 speed hub, that actually replaced a fixie wheel. Which also means you can freely ignore my manly bullshit about riding fixed above. 😁