Why? Nobody wants a flexible wheel. Not even on a wheelbarrow. The only flexible part of the bike should be the suspension. Cast alloy wheels were invented to improve rigidity and make them more reliably circular.
It was the late, great, motorcycle racer and engineer Peter Williams who is credited with inventing solid cast alloy wheels for motorcycles. His wheels made their public debut on the race track in 1970, fitted to his Arter Matchless dubbed "Wagonwheels". The reason he did so was to create a stiffer wheel with less run-out than the spoked wheels of the day. He wanted greater wheel rigidity because his wire spoked wheels were flexing when heeled over in the undulating corners of the Isle of Man TT course, sending the bike off-line. With the stiffer mag wheels, he could hold full throttle through corners where he couldn't previously.
It was rigidity rather than weight reduction that he was trying to achieve initially, although I'm sure he was aware of the potential for light weight from the outset. I remember seeing a photo of his first set of prototype solid wheels in a bike magazine many years ago. I have a vague recollection that they were fitted to a Norton in 1968. I can't find that article or picture now, but the wheels were quite chunky with 6 massively thick spokes like flanged beams. I think the article said they were actually heavier than the wire spoked wheels they replaced, but a whole lot stiffer. It was only through design refinement in subsequent years that they became lighter than spoked wheels.