Neither club has the will to leave the area if they did they would already have gone. One stadium makes much better sense from every perspective except football fans have some weird idea that if they share bricks and mortar it will destroy the soul of their club which I've never understood.
Liverpool don't have the will and won't leave the area but Everton would and very nearly did.
As well as the supporters opposing it there are practical reasons stopping a shared stadium, such as Everton not being able to afford a garden shed. The only was a shared stadium could work would be if it was publicly funded and I'm not sure how that would be in the public's interest.
Regarding your initial point, I'm still not too sure how having 2 stadiums in the area is any different to the local residents compared with one shared stadium. You've still got the same amount of people coming into the area at exactly the same times, causing just as much disturbance as before.
edit: As for the "it works in Italy" argument. It works there because the stadiums are owned by the City rather than the football clubs.