There is no universally "bad" or "good" turbulent flow. Outside of Hollywood movies or clumsy propaganda, it's always a mixture of good and bad.
Take those vortex generators: They increase the thickness of the boundary layer and, therefore, friction-induced losses, so their added turbulence is mostly bad. But if you have trouble with oscillating shocks or early flow separation on the outer wing, they can remove the last obstacle to certification. For a few minutes in a hours-long flight this added turbulence becomes good and those vortex generators become indispensable.
A rough surface takes energy from the boundary layer, so doesn't a slow, "tired" and thick boundary layer have too little momentum to fight against an adverse pressure gradient?
Yes, it does, but not always. Large, fast airplanes have wing Reynolds numbers where laminar flow is insignificant. Gliders, on the other hand, can be very sensitive to this phenomenon. Modern glider airfoils, on the other hand, take this into consideration and are rather insensitive to added roughness or bugs. Make no mistake, this early transition costs performance, but handling remains largely unchanged with those modern airfoils.