Why is the rate of reaction of polar EAS favored by inductive effects and the rate of less polar EAS reactions through hyperconjugation?
I may be oversimplifying things. 



A look at electron density


Let's pick up the extreme cases of the substituted benzenes . $$\ce{A -&gt; ArCH3}$$  
$$\ce{D -&gt; Ar(CH3)_3}$$
 
Case A shows the maximum hyperconjugation. Case D on the other has the maximum +I effect.

For a moment let's imagine that the electrons are coins. 
Case D , has more coins, more methyl groups (let's say 3). 
Case A, on the other hand has 1 coin , hyperconjugation would simply mean that I am  simply moving that coin in circles. It's simply redistribution of electrons.it doesn't actually increase the density.

So the first point which I'm going to use to answer the question is that -


Inductive effects increases  the electron density, hyperconjugation simply redistributes the electron density.




A look at Coulomb's law

$$\ce{ F \propto Q_1*Q_2}$$


More polar reactants will have a greater charge on them as compared with less polar reactants.
Since inductive effects concentrate  electron density at one area the negative charge concentration will be greater.




HOMO/LUMO

Unoccupied orbitals are high in energy and occupied orbitals are low in energy. For the best overlap the energy gap between the HOMO and LUMO must be small.



Rate Order for more polar reactions

In more polar reactions the electrostatic forces of attractions play the primary role as the polar reactants is highly charged. As established earlier ,inductive effects lead to a electron density thus a greater pull. Homo/Lumo interactions are secondary as the overlapping happens after a collision occurs.  


The electrostatic forces are pulling the benzene and reactant. That would by itself increases the number of collisions. 
A greater electron density leads to the better stabilization of the +tive charge on the reactant.


inductive effects support more polar reactions



Rate order for less polar reactions

The electrostatic forces of attraction are lower in the case as as the reactant is less charged. 
So the control of the reaction is primarily through Homo/Lumo interactions.


Unoccupied orbitals of the reactant are high in energy.( They are Unoccupied).
To bridge the HOMO/LUMO gap the Lumo of benzene carbon must be high in energy. Non bonded electrons or the electrons which are delocalized through hyperconjugation are high in energy as they are held by only one atom. 
So the HOMO/Lumo gap reduces in the case of hyperconjugation thus hyperconjugation supports less polar reactions.