Tax Cuts Affect on Economy?
Tax falls out of the equation.


Based on your model, tax can still be in the equation, but it is hidden inside of your $C$ and $G$.

First, as you mentioned, if consumption is not constant, then adjusting the tax rate will change $C$ (lower $T$ higher $C$). 

But the tax rate is also imbued in your $G$- the government must have some budget. In a balanced budget, $G=T$, which can be a model constraint.

We may not impose $G=T$, but suppose revenue must be a tenth of government spending; $$G = \frac{T}{10}$$

Thus, lower taxes must lower government spending (thus lowering $Y$), or imply higher taxes in the future (See Ricardian equivalence)


  giving individuals massive tax cuts should influence them to consume and/or save more money


This is true, but we must consider the effects on $G$ and a looming future $\tau$ due to massive tax cuts now.