NES (1983) -> SNES (1990); 7 years.
SNES (1990) -> N64 (1996); 6 years.
N64 (1996) -> GCN (2001); 5 years.
GCN (2001) -> Wii (2006); 5 years.
Wii (2006) -> Wii U (2012); 6 years
Wii U (11/2012) -> NS (03/2017); 4.33 years.
Average cycle: 5.555 years.
Then if we go to their handhelds:
GB (1989) -> GBC (1998); 9 years.
GBC (11/1998) -> GBA (06/2001); 2.5 years.
GBA (06/2001) -> DS (11/2004); 3.5 years.
DS (11/2004) -> 3DS (03/2011); 6.33 years.
3DS (2011) -> NS (2017); 6 years.
Average cycle: 5.466 years
(If you view the Game Boy Color as part of the original Game Boy and think the Game Boy Advance was the true successor, then the average cycle goes up to 6.8325 years.)
So accounting for the clusterfuck that is the Game Boy family, since those launches were all over the place, the average cycle between systems is somewhere within the 5-7 year range.
Nintendo has already stated numerous times they want to break the past pattern (longer cycle) of their previous consoles with the Switch. So that would put it past the 7 year mark, which would be March 2024. So it's looking more and more like Holiday 2024 is the earliest it will launch, they may even stretch it to March 2025 depending on how the software lineup and development looks like.
Hardware Comparison Threads:
Current Thread
Switch 1 '25 vs DS '11, 3DS '17, and Wii '12
Older Threads:
PlayStation/Xbox/Switch: 2022 Edition
PlayStation/Xbox/Switch Hardware Battle: 2021 Edition!
PlayStation 4/Xbox One/Nintendo Switch: 2019 vs. 2020
PlayStation 4/Xbox One/Nintendo Switch: 2018 vs. 2019
PlayStation 4/Xbox One/Nintendo Switch: 2017 vs. 2018
PlayStation 4: 2015 vs. 2016 vs. 2017