Speaking as an American, I have to say that the show simply doesn't appeal... Or at least didn't. It took the Daleks to get me even interested. And you're right, it's not made for us. But you should care if Americans don't get interested. Why? Because if you can reach the American Market, you'll top anything. That's well understood by the BBC.
However, the show has been gaining here in America. I know people I show earlier episodes to have backed off the show, but as soon as I show them Series 5, they're hooked. It's something about the new direction of the show.
I don't believe Doctor Who will ever be as popular in the US as it is in the UK. But does it have to be? Doctor Who is already making a big enough splash in America. The premiere screening of season 6 in America could rival the opening night screenings some movies get, and plenty of main-stream high-rated television shows like The Simpsons, Family Guy and The Big Bang Theory have included Doctor Who referances.
And all this without a bloody reboot. Hell, in the case of The Simpsons, they've been doing Doctor Who jokes since at least 1995. And the show wasn't even on the air back then.
The other thing is the failure of "The Movie" The only reason it failed was because it was a Made-For-TV Movie. I'm not sure how it works elsewhere, but here in the States, MFTV Movies are regarded as crap. On top of that, it did a poor job of introducing The Doctor as a character we could "get behind".
The primary failings of the telemovie are that they tried to introduce everything right away. You don't dump all that continuity in a new viewer's face all at once, you'll just confuse them. The opening sequence alone includes the Doctor introducing himself and the Master, with referances to Daleks, Skaro, Gallifrey, regeneration. We see the TARDIS, learn it's bigger on the inside, and see the sonic screwdriver.
Now compare that to RTD's approach. Within the first 15 minute of Rose we meet the Doctor, though all he says is that he's known as the Doctor, and I think we see the sonic screwdriver. We see the exterior of the TARDIS, but don't learn about the interior until later on in the episode. We then have to wait six weeks before learning of the Daleks, 13 weeks to learn about regeneration. Skaro and Gallifrey aren't referred to by name for two years, and the Master is introduced after three years. Meanwhile, who or what the Doctor is, where he's from are then doled out over the course of the series, and there are still several key facts that are either not revealed or kept vague.
That is not to say I wouldn't mind seeing an American Companion, though.
There's already
Peri. Depending on how you define "Companion" you could also say
Grace Holloway. And depending on how you define American, Captain Jack did claim to be American in Miracle Day.