I have noticed that there are many variants of game crashes that come from this game, which pains us all. It is hard to find the right solution for you. I am merely a messenger of advice for those who have the CRASH ON PLAY with no error message on the launcher. For everyone with the same issue that I had, CHECK WHAT GRAPHICS PROCESSOR/ADAPTER THE GAME IS USING!!!! For my game, it tries to use my GPU but fails to detect it, which is why my PROCESSOR is selected. If the settings show your processor as what the game will use, the game will automatically close itself once you click play because it can't detect the GPU (What kind of dumb crap is this??). Who knows, there might be different reasons for each PC, but this is another launcher crash solution for some here. (I'm using Windows 11)

Disclaimer: This was NOT my discovery. Props to @TheFoxxyMilo on this. YouTube: MiloTheGamingFox
(Thank you!)

Instructions and later, the YouTube link of where I got this solution from:

For Windows 11 users, IF YOU CAN BOOT THE FALLOUT 3 LAUNCHER SETTINGS

Step 1: Read what Fallout 3 wishes to use to launch the game via the launcher options. After this, close the game. (((((Remember what it wishes to use)))))

Step 2: Go to SETTINGS (On Windows)

Step 3: Type "Graphics Settings" in the search bar.

OR

System > Display > Graphics

Step 4: Look for BOTH "Fallout3" and "Fallout 3 Launcher" and click on their options buttons (Do one at a time)

If you don't see them:

Scroll to the top of the Graphics page and click on Browse. This PC > Whatever driver you have > Program Files (x86) > Steam > steamapps > common > Fallout 3 goty
Remember, you are only looking for the Fallout3 and Fallout 3 Launcher. Add them if they aren't there already.

Step 5: Put them both on High Performance (Notice what High Performance uses and what Fallout 3 was trying to use)

Step 6: Congrats! Now boot up the Fallout Launcher and take a look at what Fallout now wants to use. Does it use your GPU now? Boot the game with your preferred settings to find out and the game should boot up. Let everyone know the verdict in the comments if you can.

Video example/source from MiloTheGamingFox for all who are visual learners:
https://www.youtube.com/watch?v=vV71FYGD2eE&ab_channel=MiloTheGamingFox

Soooo... What on earth did we change to make it work? From my understanding, you basically just switched what the game will use to your PC's recommended, high-performance component. Fallout 3 is an old game that had far fewer requirements to play the game back then. Its old settings just don't work too well with our non-stone age Ooga Booga tech and it sucks configuration-wise. The game wants to use your GPU from my understanding but doesn't know sometimes where your cheeky GPU escaped to. If this solution didn't help, it doesn't hurt anything. The idea here is to see if you can use your GPU.

Remember, this fix attempts to help you actually boot the game. I cannot claim that this fixes Fallout's middle-finger crashes every 20 minutes while playing (similarly to New Vegas crashes). People want to game man. For the sad souls that still don't have their games fixed after this, good luck troopers. This solution worked for me after looking for help for days.