Perhaps if you're trying to get the best products from each cloud, but I doubt this would be worth it. For each cloud you are going to need to establish: accounts, payment, access control, continuous deployment, geographical locality of their DCs, distributed logging, billing (and watch out for egress costs!), etc... I cannot imagine the added complexity of doing this would overcome the benefits of doing everything with one provider.

But hey if your goal is to bill a client as much as possible by claiming that you're using the best products from each cloud, this sounds like a GREAT business idea.