My son is 5'7" and we've built up two fixie conversions.

1st) The Bianchi has a 51cm seat tube, so we compensated with a long 120mm stem and some nice Profile Design wing-style bullhorns to stretch him out on the bike. It feels great, even to me at 5"10".

2nd) A Peugeot with a 56cm seat tube, which is my nominal size. We put risers on this one for a more upright position. Again, it feels great to both of us.

So, you can make a bike fit, and it's not necessarily a compromise, if you do it right.