As a designer I would never hand over my designs to one of those chop shops. Any designer worth his salt can code his own designs. I don't trust the psd2html services to give me high-quality, semantic, robust markup and CSS.
Working with a good ux designer will completely change your understanding of the role of design in product development. They can play a pivotal role in defining and shaping your product. And yes, a person with these qualities almost invariably can also code. Understanding the underpinning technologies of the web remains nearly inextricably entwined with understanding the design potential of the web.
As an aside, I think a platonic ideal founding team would have 2-3 people who share varying degrees of business, design and technical acumen. Each person has a defined role, but they also relate to their co-founders' roles in a meaningful way. Really understanding what it means to be GREAT at something often requires educating yourself enough to become mediocre at it. Completely partitioned specialization is for companies big enough to need HR departments.
Umm...why not? You just said you'd never hand your stuff over to them, so what basis do you have for not trusting them?
I've personally had great results with several of them, much better than I've had with many designers.
Web designers that can't code are just designers. So make sure you hire a web designer for your website and you will get a better result.