Not having ready access to the various NPRMs that led to the rule as it is today, the following is more "reverse logic justification" than anything else, but....
Imagine an aircraft with a stall speed varying from 80kts at minTOW to 120kts at MaxTOW (which, all other things being equal, implies a TOW range from 64/144max to max - not far off 50%, good enough for government work). Assuming old-style V2 minima (to make the maths easier) we get a V2min of 1.2Vs or 96kts to 144kts. The stall speed ratio being the same, the alpha will be about the same, and any tests at one weight will be aerodynamically (if not inertially) representative.
Now, if our Vmca is nice and low - like stall speed for minTOW, say (nice big rudder) - then Vmca will not (all other things being equal) influence V2min nor V2. So the light weight and heavy weight takeoffs are conducted at very similar stall speed ratios - nice repeatable characteristics.
Now, if our Vmca suddenly is instead the max permissible - 1.2Vs1 - then it becomes 144kts. Since 1.1Vmca is another V2min criteria, we now find that V2min is EVERYWHERE 158.4kts. Which means our maxTOW case is flown at 1.2*1.1=1.32Vs, and that our minTOW case is being flown at a whopping 158.4/80 ..... almost 2.0*Vs.
While not in and of itself a problem, such a huge variation in V2 expressed as a stall speed ratio will make minTOW and maxTOW cases rather different beasts. Bear in mind that a 5-10% increase in MTOW is generally considered 'significant' for testing - and that's assuming the speed spreads are still quite reasonable. For this aircraft a pilot may conduct two VERY different takeoffs on the same plane, just because of changing the weight (keeping the minTOW aircraft on the ground before Vr is going to be fun, for one thing!)
There's no single p"point at that reason" to explain why there's a max on Vmc - it just happens to keep designs 'reasonable'.