I'm attempting to start a web business (Evanston Avenue), and have asked myself the exact same question.
I think the key is to find a niche. In particular, I think a one person shop could do a lot of damage being in expert in something like AWS or DevOps.
The traditional agency model is becoming tougher and tougher due to better tools like Squarespace, etc.
Exactly. Tools like Squarespace are making it tougher for traditional web development businesses.