The biggest factors are image and momentum nowadays. Had the Wii U launched with Super Mario Maker and Breath of the Wild, it would have sold bucketloads more than it did. And the Wii would have sold much worse if Wii Sports released a year after the system's launch. In that sense early exclusives are much more important than later exclusives, because they create the first real impressions of the console and those last for years.
The Wii U had the games it needed to sell well, but they came too late to save it. And even with some true killer apps at launch, Nintendo's mistakes like the bad marketing, weak CPU, and bad price would likely have kept it far from the Wii's level of success.
Also agree with the posters who said it should have continued to use the Wiimote and not try to reinvent the wheel again.
The PS4 is an interesting counterpoint to the 'exclusives sell systems' argument, because it actually took a while to start getting those amazing exclusives it has now but still sold really well without those exclusives. I remember the complaints of how bad 2014 was for so many people who had a PS4 and XB1 because very little was living up to expectations. That was when the Wii U started to get its killer exclusives like Bayonetta 2, Mario Kart, and Smash 4, but they came too late.
Exclusives sell systems when they come at the right time and in a sense blow the industry away. The last time that definitely happened was Wii Sports and Gears of War in late 2006. Wii Sports needs no introduction, and Gears just looked so much better than anything the PS3 launched with it gave Microsoft a huge edge for much of the generation. Had it released the following year, however, it wouldn't have had the same impact and the 360 likely wouldn't have had sold as well as it did overall.
Final Fantasy 7 is the game that put the PS1 ahead of the N64, which was actually outselling the Sony machine before then. Sonic allowed Sega to compete with Nintendo in the 16-bit era..
The only times late-gen exclusives really turned a console's fortune's around was Donkey Kong Country, which blew people away so much it allowed the SNES to pull ahead of the Genesis and win that generation, and Pokemon on the OG Gameboy. But other than that they don't seem to matter much. Perfect Dark and Conker didn't push the N64 the way DKC did. RE4 couldn't save the Gamecube. Mario 3D Land and MK7 did save the 3DS, but they came within the first year and still couldn't fully recapture the momentum that the system had lost.