This is a complete myth. The Wii actually peaked later and sold well for longer than all of Nintendo's other home consoles; except the NES, which had really weird release schedules.

1. Wii's peak month was December 2009, three years after launch. It sold a whopping 7.4 million units globally, the highest of any home console, and third highest overall - as the DS beat it twice with 7.5 and 7.8M sales.
2. Total sales for the Wii peaked in its third year after release. Total sales for the SNES and N64 peaked in their second years after release.
3. Wii continued to sell over 2 million until its 7th year in the US, and 6th in Europe. SNES and N64, both until their 6th year in the US, and 4th year in Europe. I'll note that the SNES would have dropped below 2 million in its third year.
4. The SNES's last game to sell above 5 million was Donkey Kong Country 2 , released in 1995. The last game to sell 500K was Donkey Kong Country 3, released November 23rd 1996 (granted, it sold nearly 4 million, but no game released after it would sell above 500K, Kirby's Dreamland 3 came closest at 360,000) - The Wii's last game to sell 10 million was Just Dance 3 released in October 2011, and the last game to exceed 1 million was Just Dance 2017, released October 25th 2016 - nearly 10 years after the Wii release.
5. The SNES was dead outside of Japan after 6 years, with no new releases after 1997. The Wii, after 7 years of release, in 2013 still had fairly good annual support - even if it was just family, sports, fitness, and party games, these still sold in the millions - FAR healthier than the SNES at this point. And after 11 years on the market, it's still not quite dead yet! Just Dance 2018 will probably be the final game for the console, scheduled for release this October. The funny thing about it is that it will probably sell fairly decently.

Comparatively speaking, the Wii had a healthier late-life than all of Nintendo's other home consoles... Except the NES, but a lot of that had to do with the very slow introduction it had throughout the world. Many European markets saw no official release until the same time as the SNES.

I had a thread from a while back (can't find it now) with a discussion about how, instead of releasing the Wii U, Nintendo may have been more financially successful had they put their efforts into a Wii HD, or even continued supporting the Wii until they were ready for a console like the Switch -- which, in reality, is probably where they would have gone had all the tech been there by the end of 2010. The Wii U was a stopgap, similar to the Gamecube.

http://www.neogaf.com/forum/showthread.php?t=701305

The myth is that Wii sold well for three years and then next to nothing afterwards. I am also looking at calendar years to determine the peak, not individual months. Additionally, I said sales curve which isn't something you address with your third point; Wii may have sold above 2m units longer than the SNES and N64, but the Wii also peaked higher than both of those systems. So this advantage of the Wii doesn't result in a different sales curve.