Being able to fly quickly can be a big advantage as Romulus has pointed out but what he does not mention is that a supersonic capability brings with it disadvantages which have to be weighed against the advantage of more speed.
You do not necessarily go supersonic if you have a lot of thrust. (The Harrier has a similar static thrust to an F-16 for example and about the same as a Sea King rotor in the hover). You go supersonic by using an engine designed for supersonic speeds - that is one which offers much higher exhaust velocities (blows out the back faster than you want to go forward if you will).
Taking the three types above the F-16 takes in a small mass of air and gives it a very high velocity, the Harrier takes in much more air and gives it only a moderate velocity while a Sea King rotor takes in an enormous mass of air and gives it a small velocity. In all cases the product of the M and the V is the same (round terms 18-20,000 lb).
The problem with high exhaust gas temperatures is that they reduce the propulsive efficiency of the engine (or if you prefer increase the specific fuel consumption) reducing your time at combat thrust by as much as a factor of 2.5 -3. Indeed when Harry Blot USMC took on the supersonic fighters of the day in the early 70s with his new AV-8A on an ACM range people were surprised when the supersonic jets called bingo and Harry said OK I will wait for the next lot to come out and join me.
There are other disadvantages to using a supersonic capable aircraft at subsonic speeds compared to one optimised aerodynamically at say .8-9M. Then there is the issue of whether any external stores are cleared for supersonics at low level (some just don’t like getting hot) to say nothing of the need for a lot more IR defences if you are pushing yourself along with very hot air.
Many people refuse to believe that the Pegasus in the Harrier produces a moderate velocity quite cool exhaust (even when you point out that it does its VTO from a standing start on rubber tyres). The USMC flight deck crews back in the early 70s wanted to take cover in the island when an AV-8A came in to land. I was so frustrated that I got them to chain one down with nozzles aft, run the donk at full chat while I walked through the exhaust just behind the tail. A while later I asked an FDO how close he was happy to stand to a VL he replied “Just far enough away to make sure he does not hit me with the thing”.
I must stop - this is not a subject for a quick post