The movie wouldn't have been made with Depp hadn't had a major role in it, so he'd have to be playing The Lone Ranger if he wanted a real Native American to play Tonto. I like this setup better, with The Lone Ranger being much younger than Tonto, who can be more of a mentor figure now. Depp's too old to play the greenhorn.
And yeah, the way he talks is a bit cringeworthy isn't it? Youch. But the majority of moviegoers for this movie, or any big Hollywood movie nowadays, aren't Americans and many will be reading subtitles and wouldn't get that there's something wrong with the way Depp is speaking, so they'll happily watch this thing without knowing or caring about any PC issues.