I am using 35gb on my PS3. I assure you. I can not do what I want on the Wii in terms of storage.
There would be no real reason to stuff it full of HD video given that it doesn't output HD now is there. Its also not trying to be your music player. The Wii is not trying to be a PS3. The photo channel is not there to be your photo repository. Its so you can conveniently toss the SD card from your camera in and show some pictures. Its not iPhoto. When you wrap your head around that fact, then you'll stop saying stuff that doesn't make sense. Nintendo is not trying to become your entertainment center or media server. At least not this generation.
The fact that it can't do what it doesn't need or want to do is hardly a handicap.
Now the downloadable games IS an issue for the Wii. But downloadables can be relatively easily resolved simply by allowing the system to run downloadables from SD cards. It can be solved better by allowing usb mass storage, but at this stage that's probably not required. Not that it can't happen next year. Hell they could even enable networking, on demand downloading, or even offer online storage space on nintendo servers.
And they wouldn't even need to offer a lot of space, since most of the content is theirs. (ie they don't need to stick a unique copy of F-Zero X in everyone's space.) A game like mario bros could downloaded on demand nearly instantly. And even a large N64 game could be delivered in a minute or so. The Wii could use local space as 'cache' for your hosted content. So if your playing the same games often they'll be instant. And you'd have to be cycling through a lot of big N64 games in rapid succession to really start causing the cache hit rate to be an issue. Especially as it would clearly favor holding onto larger downloads longer.
(Yes I concede the current download speeds of the Wii VC content are well below technical limitations, and so must either be artificial, or due to inadequate infrastructure at the backend (which wouldn't be surprising given the Wii's unexpected level of success. But I expect that if they wanted/needed to dramatically speed up content delivery from their online service that it would be entirely feasible.)
If a game is large enough that it can't really be reasonably put on VC then it will be released as a 'budget game' at 20 bucks, or it will be bundled into a collection and sold. Wii ware is for small games, that focus on 'innovative gameplay'.