The assumption should be that it would support ALL commonly used video inputs and that include HDMI. Nintendo was taking a risk by not including it in the first place. Obviously the successor HAS to support it. TV has changed. Nintendo has to adapt.
Nintendo took some big risks this generation, but not supporting HD was absolutely not one of those risks. It was actually the safest and least risky course to choose. Supporting HD made the PS3 and 360 insanely expensive consoles, and it made development costs a lot higher. These were risks Nintendo didn't take, but the competition did, and we see how things have worked out.
The Wii wouldn't be as successful as it is now if it had included HD and the reason is because both the console and the games would have been much more costly as a result. Aside from the motion controls, the big thing the Wii had going for it was it only cost $249 when its competitors were $500 or even $600. I don't care how much better graphics look, no one wants to spend lots of money on video games.
Look at every generation of video gaming and you will see the weakest system has always pulled ahead. It isn't because gamers hate the best graphics, its because they love the best price. Weaker consoles almost always cost less, and therefore they are more appealing to consumers.
So this was not only not a risk for Nintendo to leave HD out, but it would have been TAKING A RISK if Nintendo had included it. Becuase if they did the console would have likely cost $100 more (and/or been sold at a loss), and the MSRP of the games would be $60 instead of $49. Both of those factors would have made the Wii less attractive to consumers, and the higher development cost of doing HD would have diminished turd party support. I know the turd parties suck and are treating the Wii like a toilet which they dump their shovelware on, but if the games were expensive to make then that shovelware wouldn't be there. We wouldn't have quality games, what we would have is nothing at all. So I guess at least this way we are getting cheaply and quickly made shovelware instead of nothing, ala the GC.
And as for your comment about HD having HDMI connections, okay, but who cares? Every HD TV I've seen does indeed have HDMI ports, but you know what? Every HD tv also has RCA and component connections as well. Connecting a Wii to an HD tv is never an issue. And most people still do not own HD tvs, and back in 2006 that was certainly even more true.
So again, this was a shrewd move on Nintendo's party. They were playing it safe actually. It is the inclusion of HD that would have been the bigger gamble, and it is a gamble the competition has lost. As the facts will prove...