The valves are there to stop the original weak heater matrix bursting.
If the matrix has been changed fairly recently, it will be a stronger one, so the valves aren't needed
If the car is still on the original matrix, then it can't be in too good shape and will probably need to be replaced soon anyway. Once it's replaced the valves won't be needed.
If you don't want to replace the matrix (it's a fairly long job but doable DIY), or can't be sure whether it has ever been replaced, then you have to chop your shiny hoses and put the valves in.
The valves tend to get blocked and restrict water to the heater matrix, thus bypassing it completely. I wouldn't think removing them would cause the car to overheat unless there was a blockage in the matrix itself? Was the system bled correctly when you refilled with coolant after fitting the hoses?