Not to shoot down the idea, but with the Wii U on the way (which Amazon seems candid on ignoring for some peculiar reason...), I doubt they'l look into giving too much support to an older video game console. By all means continue on with the petition, my statement is more of a "you can try, but success is unlikely" sort'a deal.
That aside, if you'd be willing to pay for a service good ol' Netflix is 100% compatible with the Wii. I wouldn't doubt there's some not-as-perfect free streaming sites which are Wii-compatible, though I don't know of any since I'm not huge on streaming. Hate t' give such generic advice, but... Keep on google-ing lol. Best of luck to ya's findin' that proper stream site.