Density of air is defined as mass per unit volume .
Density reduces with height .
To get the lift ,we need certain density .
To get that density we fly a present speed (IAS.)
So , if you fly the constant IAS , irrespective of your density altitude , the lift will not change .
It is just because of density being less , drag component will reduce thus the TAS will increase .
Now let's talk about control effectivity ..
Suppose there is no air , control will have no effect .
Similarly when aircraft is stationary , control will move but will not produce enough forces to create couple to move the aircraft along its axises .
To get that we need to increase speed , so that density which it is encountering or mass per unit volume of air will increase , that will make the controls effective .
The first speed, which we comes into existence after rolling for take off is VMCG .
We can also say that we need more density to increase control effectivity .
So if can say that with the increase in density altitude , which we would say decrease in density per unit volume ..
The control effectivity will decrease .
Please note that VMCG is not to get enough lift to get airborne .