You’re really cutting me off at the knees with rule #2

Let’s see…

NES - VS. Excitebike
SNES - Final Fantasy VI
N64 - Super Mario 64
GCN - Metroid Prime
Wii - Xenoblade Chronicles
WiiU - Mario Kart 8
Switch - The Legend of Zelda: Breath of the Wild
GBC - Tetris DX
GBA - Castlevania: Aria of Sorrow
DS - Elite Beat Agents
3DS - Resident Evil Revelations

Atari 2600 - River Raid
Jaguar - Tempest 2000

Game Gear - Vampire: Master of Darkness
Genesis - Shining Force
Saturn - Panzer Dragoon
Dreamcast - SoulCalibur

PS1 - Tomb Raider
PS2 - Ico
PS3 - Demon's Souls
PS4 - Elden Ring
PS5 - Astro Bot
PSP - Killzone: Liberation
PSV- Wipeout 2048

Xbox - Halo: Combat Evolved
Xbox 360 - BioShock
Xbox One - Ori and the Will of the Wisps
Xbox Series - Dead Space (2023)

PC - Deus Ex

NES - Super Mario Bros 3

SNES - Chrono Trigger

N64 - The Legend of Zelda: Ocarina of Time

GC - The Legend Of Zelda: The Wind Waker

Wii - Super Mario Galaxy 2

WiiU - The Legend Of Zelda: Breath of the Wild

Switch - Fire Emblem: Three Houses

GB - Pokémon Red

GBC - Pokémon Silver

GBA - Pokémon Fire Red

DS - Harvest Moon: Grand Bazaar

3DS - Fire Emblem: Awakening

PS1 - Harvest Moon: Back to the Nature

PS2 - Persona 4

PS3 - The Elder Scrolls V: Skyrim

PS4 - Persona 5 Royal

PS5 - Black Myth Wukong

PSP - Final Fantasy Tactics

PS Vita - Persona 4: Golden

Xbox - Shenmue 2

Xbox 360 - Blue Dragon

Xbox One - Sunset Overdrive

Great List! But you broke rule number2: Not using the same franchise across different platforms with e.g. Zelda or Pokémon. The fun of this exercise is to think in what to prioritize. What would you choose if you can only choose ONE franchise only ONE time? What would the choices be?

Yes, it brings in another dimension. To prioritize the games within a certain franchise. Simply more fun to think about.

I'll do the most modern few as well as PC.

Ps5 - The Witcher 3 patched
PC - Divinity OS 2
Ps4 - Sekiro/Bloodborne, could go either way
Switch - Fire Emblem 3 houses

Also, these rules hurt cause The Witcher 3 is the best game on all those systems. 

PS1 - Metal Gear Solid
PS2 - We Love Katamari
PS3 - Bioshock
PS4 - Persona 5 (haven't played Royal yet)
PS5 - Astro Bot
PS Vita - Tearaway

SNES - Chrono Trigger
N64 - Zelda Ocarina of Time
Gamecube - Pikmin
Wii - Super Mario Galaxy
Wii U - Splatoon
3DS - Kid Icarus Uprising
Switch - DK Tropical Freeze

GB - Super Mario Land 2
N64 - Diddy Kong Racing
GBA - Pokémon Fire Red
GC - Smash Bros Melee
Wii - Wii Sports
DS - AC: Wild World
3DS - Ocarina of Time
WiiU - Mario Kart 8
Switch - Fire Emblem Three Houses

PS1 - Crash Team Racing
PS2 - SSX Tricky
PSP - GTA Liberty City Stories
PS3 - Ratchet Crack in Time
Vita - Persona 4 Golden
PS4 - God of War

Xbox - Star Wars Knights of the Old Republic
Xbox 360 - Mass Effect
Xbox One - Forza Horizon 4

Before I read the only one game per series I had a lot of mario kart in the list, pokemon and mario odyssey.

NES: Duck Hunt
GB: Pokemon Red
SNES: Donkey Kong Country
GBC: Megaman Extreme
N64: StarFox 64
GBA: Phoenix Wright: Ace Attorney
NGC: Metroid Prime
DS: Mario Kart DS
Wii: Super Mario Galaxy
3DS: Super Smash Bros 4
Wii U: Pikmin 3
Switch: TLoZ Tears of Kingdom

PS1: Crash Bandicoot 3 Warped 
PS2: Ape Escape 3
PSP: God of War: Chain of Olympus
PS3: Ghostbusters: The Videogame
PSVita: Sly Cooper: Thieves in time
PS4: The Witcher 3
PS5: Baldur's Gate 3

Xbox: Tom Clancy: Splinter Cell
Xbox 360: Banjo Tooie
Xbox One: GTA V
Xbox Series: Elden Ring

MasterSystem: Castle of Illusion
Genesis: Mortal Kombat
Saturn: Resident Evil
GameGear: Battletoads
Dreamcast: Sonic Adventure 2

GOG: Diablo 1

Steam: Robin Hood: The Legend of Sherwood 

Epic: Claire Obscur: Expedition 33

HA nailed it!

I put that 'Rule' in to give it at bit of twist to support diversity. Great list by the way!

Nintendo systems will be hard to pick as I mostly play the same franchises on those, but here it goes.

NES - Super Mario Bros. 3
SMS - Fantasy Zone 2
GB - The Legend of Zelda: Link's Awakening

SMD - Sonic the Hedgehog 2
SNES - Earthbound
GBC - Pokemon Crystal

PS1 - The Legend of Dragoon
N64 - Banjo Kazooie
GBA - Wario Land 4

PS2 - Shadow of the Colossus
GC - Resident Evil 4 (cheating here, played on PS2, but won't leave RE out of this, lol)
NDS - Digimon World: Dawn
PSP - God of War: Ghost of Sparta

PS3 - Demon's Souls
PSV - Disgaea 4: A Promise Revisited
3DS - Persona Q - Shadow of the Labyrinth

NWU - Mario Kart 8
PS4 - The Last of Us: Part II
NS - Kirby and the Forgotten Land
^ probably going to be some Xenoblade but still didn't play any, and all other IPs I have there are already gone lol)

PS5 - Gran Turismo 7
PC - Diablo