There's no reason to end that belief, data clearly shows Playstation consoles are long-lasting, it's an indisputable fact. Xbox 360 being the console with the best legs.
As for the actual post-successor focus of your thread, this boils down to PS4 vs 3DS which you could have put the data for in your OP.
3DS post successor sales were 11.3m, meaning the ps4 needs to get to 125.1m lifetime sales to beat it's post successor sales. It certainly won't be that easy but with PS4 support going into 2021 (Horizon 2), it's certainly not impossible either.
PS3 managed 8.19m post successor, 11.3m for PS4 post successor is easily feasible.
60/40 in favour of 3DS.
This is all with regard to "post-successor" sales, so a lot of your data isn't relevant. The PS3 didn't receive a successor until 7 years into it's life, the PSP didn't receive a successor until 7 years into it's life, the PS4 didn't receive a successor until 7 years into its life. PS Vita never received a successor. Using five years as an indicator really isn't helpful. What I think would be better is a graph that shows the increase in sales the the following years after the successor launched.