In short: no, and anyone who says otherwise is simply lying in order to cut off competition from potentially better fit lawyers with broader geographic footprints. Virtually every serious corporate lawyer (startup lawyers are corporate lawyers who specialize in early-stage) with a well-deserved brand has clients across city and state lines.
Because the vast majority of startups are incorporated in Delaware, Delaware corporate law governs 99% of the issues they’ll deal with. The 1% will be labor/employment issues, which will typically be governed by the location of their employees (often multiple states), and local labor boutiques are easily engaged for that.
In fact, when you’re navigating negotiations with potentially influential local investors whose ‘reach’ covers a lot of the local legal market, there can be benefits to having counsel from someone more detached from the local community. See: How to avoid “captive” company counsel.
Go through the above-linked checklist to ensure you are engaging counsel that is the right fit for what you’re building – in terms of specialization, cost structure, culture, etc. – regardless of where they are physically located.