Would it be 'wrong' to turn this rotrax into a fixed gear?

A complete barely ridden classic geared bike would be sweet as!

For me the whole concept of riding fixed is mostly about not being able to afford or maintain gears.

Keep that bike as what it is, if you want to ride fixed either sell it ( youll get a decent price condsidering condition/paperwork etc) or check the hub for a flopside which most older hubs have for 'winter training use' Stick on a track sprocket and use a different chain for riding fixed but be sure not to hipsterize your bike or throw away parts. Leave the drop/hood brake levers on & two brakes. Keep it classy.

You'll have the option then of conveniently changing it back, which you may want to do for long summer rides.

Chris Hoy can surely afford some gears by now? ;)