Why does pH decrease when diluting a base?
You are overcomplicating it. The concept of pH and pOH stems from the concentration of $\ce{OH-}$ or $\ce{H+}$ per solvent unit $\ce{H2O}$, like so $\ce{\frac{[OH-]}{[H2O]}}$ or $\ce{\frac{[H+]}{[H2O]}}$. There is also a logarithm involved, but lets keep it simpler than that. You are adding far more of the denominator than the numerator, hence the fraction is becoming smaller and the pH is going towards pH of pure water.