There probably is a market, but it's a lot smaller than building general web/mobile applications.
The kind of clients that want to build an API 1) already have a main product/website and 2) are likely more technical than average. It's probably something they could do themselves.
You're probably right, the market is probably quite small right now. But! I feel as though that might be changing... and quite honestly, I feel like the clients may very well be both businesses that are established and want to have more of an omni-presence, but also the more technical ones.
The kind of clients that want to build an API 1) already have a main product/website and 2) are likely more technical than average. It's probably something they could do themselves.