Alphabet Reduction Step in PCP Proof
The alphabet size corresponds to the query complexity of the PCP verifier. So you need to make it a constant eventually so that the PCP has constant query complexity, as stated in the PCP theorem.

And if I am not mistaken, the alphabet size increases from $\left|\Sigma\right|$ to $\Omega(\left|\Sigma\right|^c)$ for some constant $c$ in each graph powering step. If you do not make the alphabet reduction in middle steps, the alphabet size will blow up exponentially within a logarithmic number of iterations.