Honestly I think the OP is a false premise to begin with. Basically I think there is this (false) belief that somehow by supporting your previous system well it means your next system will do well because of brand loyalty or something.
But it's really not true if you actually look at it. In fact, the most successful modern Nintendo systems and the most successful Microsoft console all stem from those companies prematurely killing off the preceding system.
The DS was a massive success after Nintendo prematurely killed off the GBA.
The Wii was a massive success after Nintendo basically stopped supporting the GameCube after 2004/2005 and held off Zelda: Twilight Princess (the one big game GCN owners had been dreaming of) to be a Wii launch title.
The Switch was a massive success after Nintendo canned the Wii U around 2016 and repurposed a majority of its notable library for Switch.
The XBox 360 is by far Microsoft's biggest console success, but it came after flat out discontinuing the original XBox after 2004.
Conversely the DS and PS2 which no one can really argue had many years of support had big problems with their successors (3DS and PS3) especially early on, which shows no one cares what you did last generation cycle the moment the new one starts. This is a "what have you done for me lately" business, you don't get extra brownie points if you make mistakes with any product just because you did good things in the past.
People always bring up Sega, but Sega's examples were extreme, they release the Sega CD in 1992 and stopped supporting it basically by 1994. Then released the 32X and stopped supporting it after 6 months. Then released Saturn in 1994/95 and were already moving on to Dreamcast by 1998.
If anything I think there are examples of Nintendo supporting prior systems too long. The N64 for example should have had several huge late gen projects moved to the GameCube, particularly Zelda: Majora's Mask, Perfect Dark, and Conker's Bad Fur Day. For one none of these games could run on the base N64 without the RAM pack, secondly the GameCube badly needed these types of games early in its product cycle. They should have by 1999 decided to move those games to the GCN launch window and hired extra staff to work on bringing up the graphics.