I'm not sure that Sonic, Mario and Zelda can't and shouldn't be improved by bringing in more compelling narratives than the standard "save the princesses/toads/the woodland creatures" scenarios, but the transition has been demonstrated to be far easier said than done. While Mario has been content for the most part to wallow in the purity of its established formula, the new generation of Sonic games has boldly and consistently explored new horizons, with decidedly mixed results. Mixed enough that Sega has decided to go back to its roots with Sonic 4, which is where Nintendo has been all along.
That's not to say that Nintendo has never ventured outside its comfort zone. The franchise of Mario's RPGs (with the first installment admittedly created by Square) has consistently mixed up Mario's formula, and with good results. But for the most part, Nintendo seems stuck in the 80s, while other once-proud franchises blindly flail around for new ideas, eventually attempt to grab onto their cache of nostalgia like a polyester life-preserver, and are finally lost to the annals of history and the bargain bin (*cough*Mortal Kombat*cough*). Some might attribute Nintendo's recent success solely to their having a larger cache of nostalgia than most to fall back on, but I believe an equally important factor is that for three decades they have been perfecting a way of doing their thing, while by comparison Sonic only ever kind of worked in 3D, and Sega apparently lost the formula after Sonic Adventure 2. It would be ironic foreshadowing if an employee dropped it down the toilet.
I think most would be willing to grant me that games like Mario Galaxy and Mario 64 essentially have no story, and it's clear that although the ideal goal should probably be a good story, no story seems easily to trump a bad one. Back in the day, games like Super Turrican and Ninja Gaiden and Castlevania and Ecco the Dolphin and Zelda felt super epic because their lack of a fleshed-out narrative, and their simpler graphics, forced and invited us to fill in the gaps with our own imaginations. Another World exploited that simplicity and subtlety to create one of the most narratively rich and compelling games I've ever played. As graphics improved, and as it became easier to incorporate story into games with things like spoken dialogue and better cutscenes, gaming worlds began to feel less epic and expansive, and the stories started to sound dumber and dumber as they began to be told more explicitly and completely. We finally saw our beloved franchises recreated in glorious technicolor and quietly said to ourselves "is that it?"
I personally have no idea what the plot for Super Turrican was, but I do not wish to go and find out. It cannot possibly measure up to the fabulous mythology I build for myself as a six-year-old boy, spurred on by the captivating music and 16-bit graphics.