I would imagine that the FPGA would not be shared. Much like only one app can be full-screen on your computer, only one process could use the FPGA. The OS wouldn't let a second process use it if a first process already was.
As for regular users, personally I'd like it for video codecs. I'd like it for video transcoding. I'd like it for faster MP3 encoding. I'd like it for Photoshop filters. I'd like it for speech recognition. I'm sure I could think of things that other users would like to use it for, like 3D rendering. I don't know of dedicated silicon that does ANY of these things, except specifically for H.264 decoding. That's it. And the thing is, for all the items I've listed, it's totally fine that my computer is only ever doing one of them at a time. These are all "regular user" uses, whereas virtualization is not needed very much for regular users.
Most of the uses that you mention involve processing large (ish) amounts of data, and that's one of the drawbacks to GPUs. They're great as long as everything fits into the amount of RAM on the card. Otherwise you're limited by the PCI bus and you're constantly shuttling data back and forth from main memory. It's frustrating when you only have 6GB of RAM on the GPU and 96 or more attached to the CPU. They're just not that good at data processing.
As for regular users, personally I'd like it for video codecs. I'd like it for video transcoding. I'd like it for faster MP3 encoding. I'd like it for Photoshop filters. I'd like it for speech recognition. I'm sure I could think of things that other users would like to use it for, like 3D rendering. I don't know of dedicated silicon that does ANY of these things, except specifically for H.264 decoding. That's it. And the thing is, for all the items I've listed, it's totally fine that my computer is only ever doing one of them at a time. These are all "regular user" uses, whereas virtualization is not needed very much for regular users.