I've been thinking about this a lot since I saw the question first posed--the Wii (and the Wii U) were an odd time for Nintendo. Commercially, the GCN was not a knockout success, though many of its games seem more revered today than at release...this could be somewhat situational though as I was in high school for most of the GCN's lifespan. Nintendo games were not really seen as being 'cool'. I owned one and enjoyed it, but many around me were much more interested in the Grand Theft Auto series, Halo, God Of War, Counter Strike etc and Nintendo games were viewed as being too kiddy in the general perception of my fellow 16 year olds at the time.
There are many good points brought up I wanna touch on though. Light Gun games didn't die with the Wii, as another poster mentioned, they died with the CRT television. The traditional style worked using a quirk of their operation. I have a GunCon 3 and a few Playstation Move controllers as well...I know you could play Killzone 3 with it but my god the controls were awkward. Nintendo was rather forward thinking in the pointing capabilities of the Wii (though it does certainly depend a lot on setup and distance/position from the TV) in that the Sensor bar has 2 'sensors' spaced a certain distance apart from one another. The sensor bar design would be improved for larger rooms if it were wider or if the sensors could be placed individually. The PS Move used the PS3 Eye, which was a pretty decent USB camera for the time, but any game that required pointing or tracking with 2 players simultaneously suffers a lot because there's only one sensor so to speak.
In fact, I've not tried a PSVR but I know that it uses multiple Move controllers at a time, and I've heard that there are tracking issues due to the PS4 camera. I have an Oculus Rift for my PC, which comes with two individual sensors by default, officially supports a third, and though some use more there are diminishing returns. Accurate tracking involves a lot of overlap between the sensors, and it helps a lot if the controller is in view of at least two sensors at all times.
Anyway, the point of the tangent is that motion controls of the Wii variety kind of lived and died before they were really ready for primetime. There's not really any hard and fast rule as to whether or not motion controls ruin a game; it entirely depends on how well the developers worked around the issues with implementation. Metroid Prime 3 works well enough (it would be better than 2 without motion controls at all though), yet Skyward Sword maps the button for recentering your pointer in a suspiciously accessible spot...like they just knew that something about their design was inherently poorly functioning (and Skyward Sword minus the motion controls really isn't a great Zelda game either). Donkey Kong Country Returns is best played with a controller hack hack, as the position you're expected to hold the remote in, while shaking and interacting with buttons is a total non-starter what were they thinking design. The issue with waggle controls isn't really 'could that be a button press' it's 'should that be a button press'. The waggle in Mario Galaxy doesn't bother me much for that reason...the action it performs is situational and there's a button that makes Mario jump thank god.
Hardware sales of the Wii definitely were through the roof though. I'm not sure if Nintendo purposefully kept the console cheap by making it essentially a Gamecube in terms of horsepower while dumping their R&D into motion controls, or if they did it just to ensnare the casual gamer who really wasn't interested in the PS3 or Xbox 360 at full launch price since they were considerably more expensive. The trouble is, hardware sales aren't really where the profit margin is (most consoles are really sold at a slight loss upon launch). Not that Nintendo's quantity of sales didn't make them money, but they're really more interested in selling the higher-margin software...and a lot of those fair weather Wii owners owned Wii Sports and little else before the novelty wore thin. I do wonder if Nintendo had some misplaced gambles--that HDTVs wouldn't be affordable and heavily adopted a few years into the system's life, and that phones weren't going to completely take over the casual games market with their Free to Ride->Pay to Win and advertisement-based revenue. Though I'm not sure that in 2006 anybody really was thinking that smart phones would overtake the world by spending 3 or 4 years as an expensive novelty toy before transitioning into 'necessity' in the span of about 2 years.