That's not what happened.
With the exception of the launch window, due to shortages, 360 was outpacing its predecessor the entire time.
Xbox vs 360
Launch-1.5m vs 1.2m
Year 1-6.5m vs 6.8m
Year 2-5.7m vs 7.9m
Year 3-6.2m vs 10.9m
Year 4-4.1m vs 10.2m
Basically they tied for the first year (when Wii wasnt out yet) then 360 started outpacing it.
As for PS3, Wii had little to do with its sluggish sales, it was the ridiculously high price, Blu-Ray not being as big of deal as DVD and the loss of a ton of exclusives.
Wii was like Switch, great sales that were independent of the other consoles and complemented rather than competed with them.
Are you saying sales were not sluggish for PS3 and XBox360 for the first few years? Both consoles peaked in 2011 according to VGChartz numbers. How many other 2nd and 3rd place consoles peak 5-6 years after launch?
At the same time the Wii actually did peak early. Wii is up when the others are down. Then Wii is down and the others are up. That looks a whole lot like competition.
What? I never said they weren't sluggish, I said Wii wasnt the reason, I thought I made that quite clear.
You're whole premise of "360/PS3 were down when Wii was up and 360/PS3 were up when Wii was down" makes no sense when you actually look at the trends.
Why did PS3 & 360 both have ~30-40% YoY growth in Wii's peak year if Wii was the reason their sales were low?
360 & PS3 both had slower starts and peaked late but it had very little to do with Wii.