How does an inoperative Anti-Skid affect V speeds?
When you say it affects V speeds, I assume you mean V1 (and possibly VR), but not V2. V1 is usually calculated from the balanced field length, which is where accelerate-stop-distance and accelerate-go-distance are the equal:

(image source: boldmethod &gt; Engine Failure On Takeoff: Do You Stop Or Go?)
While the accelerate-go-distance will be unaffected, the accelerate-stop-distance is affected by anti-skid because you will not be able to brake as efficiently as with anti-skid operating normally:

the antiskid system stops the airplane for all runway conditions in a
shorter distance than is possible with either antiskid off or brake pedal
modulation.
[...]
Braking with Antiskid Inoperative
When the antiskid system is inoperative, the following techniques apply:

ensure that the nose wheels are on the ground and the speedbrakes are
extended before applying the brakes
initiate wheel braking using very light pedal pressure and increase
pressure as ground speed decreases
apply steady pressure and DO NOT PUMP the pedals.


(Boeing 737 NG FCTM 6.45 - Landing, emphasis mine)
As you can see from the above quote, you will increase the stopping distance compared to a normal braking with anti-skid, which results in a larger accelerate-stop-distance, which then reduces the balanced field length V1.
It has nothing to do with the brake energy limitation because the maximum energy that can be absorbed by the brakes is the kinetic energy of the aircraft at the moment you start braking. It does not really depend on how you brake, but with anti-skid inoperative there is a chance that the tires will lock up while decelerating which actually reduces the amount of energy going into the brakes and increases the energy that goes into the tires (in the worst case, this energy will then cause a tire blowout).