It's a fair question, and I suspect that other people will give a much better answer than me, but I'll give it a go.
It's not really about the ability to go supersonic, it's about having the thrust to be able to go supersonic - because that thrust is what you need for combat manoeuvering at subsonic speeds.
In a turning fight, or an evasive manoeuvre, a very major factor is the aeroplane's ability to turn - that in itself is pretty obvious, even without specialist knowledge.
Now, if you try and turn an aeroplane at a high rate, the first factor that matters is the amount of instantaneous lift you can generate. Ultimately, this is down to your speed at the start of the manoeuver, and to your aeroplane's maximum lift coefficient.
However, that instantaneous high turn rate uses a lot of energy up - so if you try flying that sort of manoeuvre in your Rans S6, for example - or in something even more gutless like a Jaguar, you'll rapidly bleed off energy, which bleeds speed, which gets you to either the stall, or in avoiding the stall, a much poorer turn rate - which may well get you shot down.
So, to maintain that high turn rate, you need to keep injecting much more energy into the aeroplane. If you are very high, you can use height loss to do that - but that's limiting for obvious reasons. The rest of the time - you need a lot of thrust to keep injecting energy into the aeroplane, and so allowing you to sustain the turn rate and avoid getting shot down.
Now if you've got that thrust, you need to maintain control of the aeroplane if it's used continuously in level flight - which essentially means that the aeroplane has to be designed with supersonic capability. But, to a large extent the supersonic capability is dictated by the thrust, which in turn is dictated by the need for continuous turning capability.
You can also add high climb rates into the equation - but the formula doesn't change much for those.
This is very simplistic, I've not used that theory in the context of a combat aircraft for years, and I'm sure that some of the real combat aircraft experts will come in and give a far more accurate answer shortly. But, I hope it helps a bit.
G