@deweyzeph,
You can't make claims like that. Yes, you can make claims that sway in that direction, but you can never say for sure. The three roles can communicate with one-another. They relate, and one cannot function without the other, unlike your example of doctors, engineers, and lawyers.
However, I agree with your intention. To have a truly amazing website, it is best to work with a firm where different tasks are delegated in an A-B-C process approach. To have the three different aspects worked on by specialists for those respective aspects is indeed the best route to take.
Side note: small businesses will always take the route of finding one person, or a two-man team to design develop their website, simply because it can be inexpensive. They just want to get out there, and don't need masters to achieve that. Once a company grows, then they can start looking for the three roles separately. But, I believe that those three roles must be found in one firm, because they work together to bring about the best end-result possible.
One more side note: I may not be a master of the three roles, but have been referenced as very good at front-end and back-end development. As for design, I could do much better, and generally start something and do the rest with the help of a colleague. This helps my colleague understand the direction I want to take, and I get to learn a few things whilst I'm at it.
@_kabal_: Love the work on the Wetherlys site. Pity they shut down though...