Absolutely not. Try something with a hub gear.
Or just a dérailleur if it has to be light ... the maintenance disadvantage of dérailleurs is ridiculously overstated.
Gotta agree about the cornering ... never raced, but still frequently had to stop pedalling as a kid to take the corner (bit more fear of the grip of my tires nowadays though). Taking it real close past a high curb is impossible too.
Well since this has apparently evolved into a discussion of bicycle gears, let's discuss that. Derailleurs are a perfect solution, and I find there are very few areas where hub gears hold a real advantage.
The point of fixed gear is not that you can't change gear ratio, that's more like a consequence... As in, traditional chain tensioners don't work on fixed gear, and a derailleur needs a chain tensioner... The point of fixed gear is being fixed (ie. no freewheel). This gives an incredible level of control at low speeds. Plus I think it's tremendous fun. Anyway, there do exist non-freewheeling hub gears, which would combine the advantages of both... That said they are heavy and expensive.
As for the pedal clearance, frames built for fixed gear have a higher bottom bracket for that specific reason. Yes, you cannot lean into a turn as much as you can with a road bike, but you likely won't be hitting speeds like with a road bike either - thus, less leaning. As for taking it "real close" to high curbs, I think that's super dangerous on ANY kind of bicycle.