You have a point with NSMB but the others? No. Mario Kart DS and Metroid Prime Hunters came out well before the DS Lite and didn't turn anything around. FFIII? Come on. It did well but it was nowhere near a huge seller (neither was Metroid for that matter).
I'm not saying the DS wouldn't have been revived without the Lite but I certainly think that the Lite kickstarted it and was a key contribution in how successful it ended up being. The sales numbers tend to back that up.
Mario Kart was released in November 2005,
NSMB, MP:h and FFIII all came out in Spring 2006 just before the DSlite came out.
If you don't see how the lineup had a tremendous effect on DS's fate I can point to December 2009 when NSMBW pushed Wii enough to give it the best december any system ever had in the US despite the market being really apathetic to it for most of 2009.
Softwares sell hardware, that's always been true before and that's still true today.
Sony did a somewhat similar job when they brought out the PSP-2000, in that PSP sales did significantly rise for a number of months, but the problem was that it was too little, too late. Development had already dried up at that point and while development did pick up once hardware sales rose, by the time those games were actually finished, the momentum was already gone again.
It was shortlived because software didn't follow it, heck Monster Hunter alone put PSP back to life in Japan.
The model of what MH offers is also pretty much what people pushing for Soul whatsisname to do well.
Again Software sells hardware.
Those two re-launches, plus the way Sony revived the PS3, are what Sony needs to look at if they've any interest in reviving the Vita.
PS3 was never really dead in the EU, it had little competition from MSFT's offering so when it reached an affordable price (along with the marketing campaign going with the slim) made it a desirable product because the software proposition was already there (look at Gran Turismo for example).
My point is that hardware revision comes with a marketing push that spurs sales, but to sustain it there needs to have software that people want to pay for.
A good example would be that this bundle with AC Liberation was a better move than simply slashing the price.