As someone who is a professional musician who started playing piano "late" (age 7), I have some definite opinions about this. (I'm not suggesting I'm more qualified somehow to talk about this or anything. Just giving my background.)
While I don't think that starting a child earlier than 7 is a bad thing, I think the expectations are generally a little different. You're generally going to see inconsistencies when a child is practicing unless you (figuratively) sit on them from time to time. That combined with the fact that most beginning piano books are, when it comes right down to it, really dull. As much as I get how pieces such as Down the Slide and Up the Slide can be used to teach ascending and descending notes and how to read musical notation, this gets old really fast. It's not really music, and it's immediately obvious to the child that this is so. A series that concentrates too much on building up technique gradually with little to no room for actual musical exploration is often met with disinterest and, sometimes, outright rebellion.
So IMHO it's a pretty tall order to expect a 6-year-old to be self motivated when it comes to getting enough of the basics to get past the musical doldrums at the beginning. The long-term rewards are not usually evident to them yet.
That said, there are plenty of music skills that you can help them develop at this age. Pitch matching and rhythm games, for instance, are remarkably effective at developing musical skills. Singing in a choir is another great one. Or, if you really want to continue to use piano as the musical medium, help your child pick out melodies that they have heard, or help them explore intervals on the piano, or... just let them sit there and mess around. It might not sound like they're doing a whole lot, but I can pretty much guarantee they're being much more audiophilic than you might think.
Best of luck to you!
I echo George_c's comments, especially the comments about interest in beginner play. When DS started showing an interest in reading music, I bought easy piano scores from soundtracks of movies he likes. The melody in those songs is no more complicated than those in the beginner books, particularly if you treat an ostinato or phrase as a separate "song" anyway, and the thrill for a young child of being able to play an immediately recognisable song from a favourite movie is rewarding.
