If each of the big 3 had a Mt. Rushmore depicting 4 characters that best represented the brand, what 4 characters would each company pick?

I'd bet it'd look something like this:

Nintendo:  Mario, Link, Donkey Kong and Pikachu.  Runner ups: Samus, Kirby.

Sony:  Crash, Kratos, Nathan Drake and Spider-Man.  Runner ups: Aloy, Trico

Microsoft:  Master Chief, Marcus Fenix, a racecar from Forza, Ori.  Runner ups: Fable character, Conker

Who would you want to see on each one?

"A racecar from Forza" LMFAO

This is what I'd LIKE to see, but not probably the best representation.

Nintendo: Mario, Tom Nook, Tingle, Waluigi
PlayStation: Captain Qwark, Daxter, Knack, Racoon from Tokyo Jungle.
Xbox: Banjo, Conker, Pinata, Minecraft Pig

To me the term Mt Rushmore is about what established the brand not what is current establishment.

Sony: Crash, Lara Croft, Solid Snake and Cloud
Microsoft: Masterchief, Marcus Fenix, (Honestly not really anything outside of this comes to mind)
Nintendo: Mario, Link, Donkey Kong and Mega-man

would you not more associate these characters with Nintendo? Given that they've had far more successful games during their time with Nintendo than with MS, unless you consider the remaster of the N64 game on the original xbox or whatever that young conker monster... I mean would you really want this face on your mountain

Good choices, I actually agree with almost all of this.  I'd probably replace Mega-man with Samus if I were to change anything, but I can definitely see why you chose Mega-man too.

I was actually leaning towards Kirby constantly instead of Mega-man and Samus, but all three are good for a fourth choice on establishing the brand that is Nintendo. 

Nintendo: Mario, Pikachu, Link, Donkey Kong. So I agree with OP's list.

Sony: Mazda Miata, Drake, Kratos, Ratchet. (Spiderman/Aloy/Ellie/etc don't have enough history to be considered to get on there, IMO)

Microsoft: Chief, Fenix, Ferrari 458. (Honestly I don't there is a fourth one that deserves to be there)

Nintendo - Mario, Samus, Link, Kirby

Sony - Ratchet, Nathan Drake, Kratos, Sweet Tooth

MS - Cole Train (WOOOH!), Master Chief, Alan Wake, Cuphead

Sony: Kratos, Nathan Drake, Sackboy and A Helghast.

Nintendo: Mario, Luigi, Pikachu, Donkey Kong.

MS: Master Chief, Marcus Fenix, Jago and Ori.

I can only fit 3 on each company.

Sony: Pilot whit GT helmet, kratos, Drake.
Nintendo: Mario, Link, Pikachu.
MS: Chief., M.Fenix, Pilot whit Forza helmet.