The high-end 'cross bikes are pure race bikes and don't have rack and fender eyelets. Something like a Cannondale CaadX, a Kona Jake, Ridley Crossbow, or a Trek CrossRip would suit your needs very well and all are under 2k. Keep in mind than any tire will get pinch flats in potholes if you don't keep the pressure high enough. As for the high bottom bracket, that's mainly a result of wider, deeper tires. If you put narrower ones on it's the same as any road bike. They could design for that height with large tires, but then the versatility of being able to use a variety of tires would be lost. You just get used to the bottom bracket height after a week or two.
A lot of people here in Saskatoon ride 'cross bikes for the same reason you want one - the roads are really bad and they don't want to plod along on a bike designed for something else. They've sort of replaced the old sport-touring bikes as the default road bike. The offshoot is a very active cyclocross race season.