Some thoughts.
This kind of service might be much more valuable to huge corporations rather than startups. BigCo, Inc. is more likely to have enough cash lying around to hire an extended team all at once. Also, BigCo, Inc. is more likely to suddenly need X, Y, and Z skills to build upon recently acquired product ABC, where hiring a team with said specialty makes sense.
My uncle has been working on the same team for roughly two decades. They've migrated between companies together countless times. I think the main reason they've been able to keep the gang together is because they have a very niche specialty (within the domain of DSP hardware). This kind of service may be more valuable for finding those kinds of niche teams, rather than general BFF web devs.