If I had to define something that "drove me nuts" about 37 Signals (although it doesn't, really), it's that the product they have worked on for the longest, and is the most visible, is their blog. The blog, and their fame, via the blog, Rails, conferences, etc... is the real barrier to entry. They say "make it really simple", and it works for them because they are way more visible than other people, who could copy much of what they've done in a relatively short amount of time (because, after all, it is simple, and "does less"). However, if I make something super simple, I don't have that visibility as a competitive advantage, and someone else could quite easily copy my simple app in no time. That is, IMO the grain of salt that they need to be taken with.
That said, they certainly do quality work, and I am eternally grateful for Rails. I hope they continue to be successful.
I think that if you dedicated your project to being as efficient in developing quick, painless processes, you'd get yourself a following pretty quickly. I think the best instance is a company like Contrast, which is very similar to 37signals in some ways but only because they follow the same process in their design. This isn't something that just one company can do.
That said, there's a big difference between having a product with very few features and having a product that's elegantly simple.
They were highly visible in the design industry even befor blogs and products. I still remember the day when they went first online. The site was innovative in it's design and featured a sort of manifesto (The 37 signals. Each signal was one blurb about how to do awesome web design.) When they changed to products, they were already well connected.
That said, they certainly do quality work, and I am eternally grateful for Rails. I hope they continue to be successful.