The problem I see, at least for scalable solutions, is that the cloud vendor would need to have an FPGA plugged into the ethernet or attached to an instance.
Doesn't seem very practical. At least for now.
Amazon manages to provide EC2 instances with GPUs. I see no reason (beyond cost and low demand!) why another provider couldn't provision some instances with FPGA accelerators.
Well for a start, if it's an FPGA that the end user can download a bitstream to configure it is really easy to burn the chip and then Amazon has to replace it.
If you sandbox it you lose some flexibility.
Also, as you said, demand and cost are the problems I think of. The regular FPGA developer usually has no idea of how to interact with the cloud.
I worked with FPGA for five years before going to python / backend. Most of FPGA people develop in windows and don't know web at all in the application layer.
I think FPGA as a service can be something really interesting. But it's really hard to find the customers. GPU programmers are software developers, whereas FPGA people aren't.