In terms of lifespan the Wii had the longest of any Nintendo home console in the west and in Japan it had the longest life of any console since the SNES. The issue of it not having games in it's last year is also very common for Nintendo consoles. The N64 and Gamecube already established the pattern of Nintendo basically dropping development of the outgoing system to focus on the next system in the final year.
I don't know how much the Wii would have had left in it if Nintendo had kept making games instead of switching over to Wii U development. While still good overall, sales were declining in 2010 even though Nintendo had an outstanding lineup that year.
The system I think Nintendo should have waited to release is the 3DS, at least by a few months. One of the reasons sales of the Wii U and 3DS tanked so badly right after launch was the lack of games. If Nintendo had waited until Ocarina of Time 3D was ready at the least the launch lineup would have been that much stronger and the wait until the next wave of games would have been much shorter, both of which would have helped the system build and keep its momentum while still allowing it to come out long before the Vita. The 3DS did recover from its initial struggles because of the price drop and a good lineup in the second half of the year, but that initial stumble I think killed its chances of reaching 100 million units sold, which I think would have been achieved if it both launched at a lower cost and did not have that initial drought after launch.
Nintendo was not able to provide enough support to their systems for 3 years. They didn't have enough games for the 3ds when it launched in the first half of 2011, though they managed to fix that by the second half of the year and kept it going for the next few years. They didn't have enough games for the Wii in 2011 and to an even greater extent in 2012, and the post-launch drought for the Wii U was legendary, with very few worthwhile games releasing in the first half of 2013. I don't think any release strategy could have saved the Wii U in the end given its price and the confusion in the market over it, but I do think it could have done Gamecube numbers of they kept some sort of momentum going with a decent release schedule after launch.