Do I need a separate page for every city I serve?

Yes for the towns you actually work in, and only if each page says something real. Google ranks a page for "roof repair in Jeffersontown" far more readily when there is a page about roof repair in Jeffersontown. A single contact page listing twenty cities does almost nothing.

The failure mode is copying one page twenty times and swapping the city name. Google calls those doorway pages and they can drag the whole site down. A page earns its place when it names real neighborhoods, mentions jobs you have done there, and speaks to what is actually different about that area, whether that is the housing stock, the soil, or the permit office. If you cannot write a few honest paragraphs about working in a town, skip the page. Building those out properly is part of local SEO for Louisville contractors.