days gone

7 days to die is an open world zombie survival game. Getting the motorcycle is a slog, it's practically an end game item. But once acquired, it's totally badass.

Lego City Undercover, Marvel Superheroes, and DC Super-Villains. Definitely not the primary gameplay focus, but all three have an open-world map that you hop on a Lego motorcycle and cruise around between levels. There's even some racing challenges here and there to put your motorbike to good use.

The original Crew. You can get it for cheap/free, slap on the TCU patch and drive motorbikes accross a spectacularly large continental US.

Sleeping Dogs - I'm pretty sure it's only on console, but imo it's absolutely worth the time and effort to track one down if you don't already have one just to play it.

Project Zomboid - while there aren't motorcycles in the base game (yet), there are a few great mods that add different types of bikes to drive around the map.

Would Days Gone count for this? It didn’t hold my attention, but it seems pretty centered around a motorbike.

Ghost Recon Wildlands/Breakpoint

You can go ahead and add Skyrim to your list

The Crew Motorfest, it's Forza Horizon with motorbikes

Death Stranding, if trike count.

I played the MX vs ATV games years ago as a kid and they were heaps of fun then. No idea what the new ones are like but legends is cheap at the moment on steam and seem to get good reviews. Definitely a more pure racing game though than the others on your list.

Does it need good driving mechanics or just motorbikes? CDDA you can build any vehicle you like, you could even make a solar powered amphibious folding ebike - just be careful not to overload the weight on it with some of the larger batteries, easier on large vehicles as you have greater displacement. Though you could make your motorbike 10m long. Width is limited as wider I think will require more than 2 wheels so not really a bike anymore.

The vehicle building system allows building what is commonly called death mobiles.

7 days to die

Fun fact about Watch Dogs (Only the first? I didn't play enough of 2):

The bikes were easy to use, and actively one of the first vehicles I, and many others, got. But Watch Dogs has an "invasion" PvP multiplayer system (or used to, that game will never be as fun filled as it was when I first played :/ ) where you would attempt to "hack" another player by following them not being noticed for a while. Thing is: NPCs can't ride motorcycles. When you are out and about on a bike, and you see someone else out and about on a bike... Best trick for finding those invaders.

Far Cry New Dawn has motorbikes with sidecars, but no straight motorbikes.

Both it, and Far Cry 5 that it is a sequel to also have quad bikes.

Potentially neither of these quite count, for the purpose you're asking the question?

Breath of the Wild, though the motorcycle is a bonus item not really an integral part of the game.

FUEL 2009

Test Drive Unlimited

If you list GTA 4 and 5 you should also list GTA 3, Vice City and San Andreas.

VEIN

Sons of the Forest. Technically.

Late game ff7 is open world and it features a small motorcycle minigame which isn't at all accessible from the world map but still it fits your description!

Also chocobos...

At least one of the modern Ghost Recon games has motorcycles.

sorry. from the title I just came to say cyberpunk. you know the one pistal will plast you into the sky if you shoot the ground yeah?

I wish Smugglers Run would get a reboot...