I remember reading in the past of various absolutely pointless but humorous inventions such as the submarine with screen hatches, and one of those items was the "pedal-powered wheel chair". I think the big issue you'd fight in perception is that a wheelchair's intended for those with trouble using their legs, a bike/trike requires the legs, so they'd ordinarily be viewed as mutually exclusive.
Another big factor is "does it look like a wheelchair". With a wheelchair, you normally sit very upright, with legs fairly close in- required so you can reach a door handle and stuff like that. So an 8' long recumbent trike has a considerably different layout.
By the way- in triathlons, they do have competitions for those in wheelchairs. They used handcycles (powered by hand crank and conventional chains, derailleurs, etc.) for the cycling part and wheelchairs (powered by hands on wheels) for the running part. The wheelchairs used are not the same as a regular wheelchair, they are made just for that purpose, but they are distinctly different from the handcycles, too.
__________________
"be careful this rando stuff is addictive and dan's the 'pusher'."