I find it difficult to disagree with the idea that Obsidian binds the player's hands right out of the start with the setup. The bullet missing anything (too) vital, being found, being taken to a skilled doctor in an irradiated wasteland.
I interpret luck in Fallout(and many similar games) as a force that actively warps reality around you. Perhaps there are many ways reality(for the game character) could go(representing other players playing the game), and high luck pushes you towards ones that are good outcomes for your character. Which seems to be about in line with how Fallout itself viewed Luck:
What happens to the courier is something I'd describe as highly lucky. And therefore I have trouble ever making a courier that doesn't have a very high luck score, I feel compelled to do this and it's not much of a choice in my eyes.Luck is the odd statistic. It is a combination of fate, karma and, in general, how the universe views you. Luck will modify many things... All characters will benefit from a high Luck, and will suffer a little more with a lower Luck.
Perhaps being able to make a character without high luck makes the game more mechanically interesting, but what if the game just assumed the courier was lucky and replaced it with a different characteristic? I think I'd quite prefer this considering the setup Obsidian gives you.
Or perhaps moving the character creation to before the setup and having the player respond to their characteristics. A high endurance character pulling themself out of their own grave and hobbling to Goodsprings just to collapse at the (metaphorical) feet of Victor, and so forth.