One reason is that any device you want to use as a lift dumper needs to be able to be instantly retracted and this is really difficult to do with a flap. On an airliner when the lift dumpers come up, if you slam the thrust back up to TO, they immediately come back down. A flap system with its slow moving drive line can't do this, and it's enough that it has to be retracted from landing to takeoff setting for a balked landing like that.
Plus, even in a normal landing, you would be landing with the flaps at the landing setting, and when you touch down they would need 10-20 seconds a typical drive system would need to move up past 0 to a fully up position. You'd be stopped by then, and deciding to take off again on the rollout is out of the question.
So you can see that any system like this would require flaps that can move up and down rapidly like ailerons. A really difficult engineering problem.
You might do this on a small airplane with manual flaps operated by a lever, but now you have to cater to twice the movement range as regular flaps, and you'd lose the mechanical leverage you'd need for manual flaps to work unless you made the lever move twice as far (by say having it move in a 180 degree arc - but now the lever handle is in the back seat).
Lots of gliders use flaps - without any spoilers - and they can in most cases be "reflexed" up a small amount, but this feature is done only to unload the trailing edge region for high speed running which has an effect similar to reducing wing area and pitching moment to reduce both induced drag and trim drag.
For approach control and landing, they actually do the opposite of what you would think; you drop the flaps down to near 90 degrees when you want to come down steeply and for the landing roll. Not everybody likes that kind of system because you have the same problem - you can't bring them up and down quickly like spoilers so you can't work the flap lever like a throttle on approach the way you normally do with regular spoilers/dive brakes, and they require different flying techniques, on which a pilot used to spoilers needs to be carefully briefed to avoid trouble.