"It's bad enough when Nintendo makes excuses. I'm really tired of that. It's even worse that so many of their fans use the same lame excuses in defending them. "They make games for everyone." "Online isn't profitable." "Quality over quantity." These are corporate excuses. They aren't valid for us gamers so don't use them. Do you have stock in Nintendo? Don't have blind faith in Nintendo. They have faults and they make mistakes that you shouldn't tolerate or make excuses for."
I think you're seriously overcompensating. Those "corporate excuses", as you call them, do hold grains of truth in them that are valid for us gamers. If you can't see that, then I doubt it's us who are blind. Quality over quantity for example... my favorite game ever is Metroid Prime, so I can't disagree with that philosophy. Of course it would be nice to have both, but in my opinion none of the consoles has an absolute advantage in both... this isn't solely a Nintendo issue.
"The SNES is what made me a Nintendo fan. Why can’t Nintendo’s new consoles be at least half as good as the SNES was? I’m not asking for Nintendo to be Sony, I’m asking for them to be Nintendo."
I'm hoping you mean in terms of choice, because I love my GC and its games a lot more than I ever loved my SNES. Nintendo does need more choice, but I think a large part of why they haven't regained that choice yet is because of Sony. Sony stole away most of their third parties after Nintendo's N64 blunder... whether you want to admit it or not, Sony is pretty damn smart, and your whole complaint seems to hinge around the hope that Sony messes up badly and Nintendo regains their lion's share. I don't see how your complaint has any solution other than praying Sony screws up.
"I’m not asking for Nintendo to be Sony, I’m asking for them to be Nintendo."
The problem with that is that Sony has usurped what Nintendo used to be, at least in terms of third party support. Asking Nintendo to be old Nintendo isn't going to work unless they can first oust Sony, and to do that they have to be better than old Nintendo. I get the feeling some of you don't realize this. Being old Nintendo when they're not in power is just going to ruin them... to act like a king again they have to reascend to the throne first, so to speak. There's no magical document hidden deep in their archives that they can find and read and realize "aha, the solution to all our problems... THIS is how we used to be!"... no, they have to bide their time, invent new weapons and engines nobody has seen before and storm the castle once Sony shows any sign of weakness.
"And before everybody chimes in saying, "Well, *I* don't care about online, online is useless, Sony and Microsoft suck, NITNEDO FOR EVAR!!!1111!!""
Hehe... by "everybody" you pretty much mean just me.

"Contrary to what many of you may think, I love my GameCube. I have more games for it than any other system. My dissatisfaction comes from the fact that I am forced to buy other systems to play games that skew towards a certain audience, or to have the "best" version of a port. That's retarded. For crying out loud Nintendo, build online into your next system (which they've done, thank God) and start developing mature* titles on a consistent basis. Nintendo would demolish all competition if they could round out their product portfolio with some software that has a little edge. How about a kick-ass new franchise with adult themes and situations? Something edgy and cool? Or has that been scrapped in favor of another Mario Tennis game or Mario Party 10? <shudder>"
So let's recap. You love your gamecube but you also love some of what Sony and Microsoft are doing, which is Nintendo's fault because no other game company should be allowed to come up with anything good. You want Sony and Microsoft to lay down like good little doggies while Nintendo walks all over them and steals any good ideas they may have contributed that could possibly appeal to anybody, so that nobody has a reason to consider getting either other console. Methinks maybe you're underestimating S&M just a tad, but anyway:
None of your proposed solutions will accomplish any of what you want. Nintendo would not "demolish all competition" by matching them... I'm sorry, now you're just being blindly hopeful and unreasonable. Even if Nintendo offers EVERYTHING the other two offer, which is impossible, your idea of "demolishing all competition" is a pipe dream you're allowing to color your judgement... why should anybody get Nintendo when the other two did it first? It may be possible that Nintendo could demolish all competition... but not the way you want them to, that's just ridiculous. They have to come up with something neither Sony or Microsoft has done before that so far outweighs their respective advantages that everybody has to have Nintendo's system.
On a not so related note, I will agree that they should make a kick-ass new franchise though. That would be cool, so long as the focus is on its newness and kick-assness and not on its maturity.