You're basically saying that you're more likely to dodge a missile traveling between mach 2 or 3 starting your maneuver at 400 knots than at 800 knots. This is nonsensical. If you're trying to dodge an SRAAM it's much better to start at mach 1.2, spend that energy budget in a tight turn that slows you down into mach 0.6, than it is to start at mach 0.6 and then try to maximize your corner radius, or accelerate into mach 1.2.
Similarly, though offensive maneuvers to acquire a lock involve more complex considerations, it's far better to start your maneuvers at mach 1.2 when you have much more energy that you can then spend in order to get into a firing position than to start at mach 0.6 to maximize your turn rate. You're only thinking in terms of transient performance as a static parameter, not in terms of the fighter's overall energy budget. It's always better to start with a higher energy budget.
This also applies to acceleration. If you're at mach 1.2, acceleration into a higher speed is of course more costly, but you're overlooking that at mach 1.2 you're already at the energy state that you're trying to reach when you're trying to accelerate from mach 0.6, and at the end of the day the whole point of accelerating is to reach that higher energy state. The missile doesn't care if you're accelerating faster or turning tighter if it's got higher relative speed than you. If your relative speed to the missile is higher your odds are always going to be better than if it's lower. That's what "bleeding energy" and "being a sitting duck" refers to. If you start your evasive maneuver traveling faster and thus being further from the missile when its launched your odds of surviving are going to be better if you start evasive maneuvering slower and closer. Higher altitude and higher speed is by definition higher energy. At those higher energy states you may bleed energy faster, but you also have more energy to bleed, and you get more out of the energy you spend.
Furthermore, an airframe that is capable of supercruise is by physical definition going to have a lower drag profile compared to a non-supercruising airframe accelerating from the same starting velocity, and may even maintain a comparable or superior drag profile accelerating from a much higher starting velocity. There is no part of this comparison where a supercruise capable airframe does not maintain a significant energy advantage over a non-supercruise airframe when it comes to kinematic characteristics.
Energy maneuverability is not just a static turn radius game. Angular and linear vectors, transient kinematics, and relative energy states all matter.
The thing you're ignoring is a G-limit on maneuverability; i.e, a faster aircraft with 9G maneuverability isn't going to be more maneuverable in angular terms than an aircraft in slower speed and with the same or higher G maneuverability. If the aircraft has a 9G STR at 400 knots and a 4G ITR at 800 knots, starting the maneuver at the same relative time to impact will be more advantageous at 400 knots.
The claim is fundamentally as nonsensical as if I were to be dodging a bus coming straight at me. On a motorcycle, I'd have reduced maneuverability since I'm already at speed, and be challenged by both the cornering ability of the motorcycle and my own cornering skills. On foot, on the other hand, I could simply side step to get out of the way of the bus.
====
In reality, when you're dodging a missile, it's going to be a BVR attempt to dodge the missile because missiles at high energy states, potential or kinetic, are going to be unevadeable. The only times you can evade the missile is when the missile is at a depleted energy state, i.e, it's been chasing you for some time. In that sense, high supersonic maneuverability is useful because you'll be in a supersonic state in an attempt to evade the missile to begin with, and you'll decelerate by using ITR to bleed energy until you're in a low-speed high-agility state.
However, the other aspect of this is the turn; i.e, when you're being homed on by a BVR missile from long-range, you need to do a 180 degree turn so you can begin evading the missile instead. A high-speed platform is going to spend considerable amounts of time bleeding energy and altering course so that it can reverse direction, i.e, at Mach 1.2, you could be spending 18 seconds at 10 degrees (9G) turn rate just to go to zero degrees, whereas a Mach 0.4 platform could do the same turn in 6 seconds.
In such a case, your best option (since you'll lose all speed as part of your original velocity) would be to decelerate to increase the angular maneuverability, then attempt to regain speed.