A tensioner won't work with fixed. Neither will leaving the chain slack (or it might for a while until it comes off). So you'd have to slacken and move the wheel to re-tension each time you changed gear. Perhaps marginally less trouble than turning the wheel around. You would probably get away with chain alignment using a flexible derailleur chain, but it would be less than optimal.
A dual fixed set up would be a solution for hubs which have a lock nut thread only on one side.
It may also have been a solution for TT riders in the 30's and 40's. I believe some riders when riding a straight out and back timetrial would ride a lower gear into a headwind and then turn the wheel to give a higher gear for the return leg. A dual fixed sprocket would be quicker than flip/flopping the rear wheel.
I've never met anyone who can set chainline to that degree of precision. You do need to reset the tension. A friend has this arrangement on her old French ladies' bike. Easy done. Racers used to do this all the time, pre derailleur.