Well that's one of the original ideas behind Fallout; the protagonist is this mysterious stranger who comes out of nowhere and either acts as a beacon of hope, a neutral wanderer, or a harbinger of destruction to the people of the wastes. Haven't you ever read one of those books or seen one of those movies where the protagonist is down on his luck, and out of nowhere comes this mysterious stranger to assist the protagonist? That's who you're supposed to be in Fallout. Granted you can be fairly neutral or even evil, but those are just two different outlooks for the same type of character.
Fallout 3 diminished this feeling quite a bit since the protagonist's father played a significant role in the plot. In fact the main quest wasn't your character's story at all; it was his or her father's told through the eyes of your character. Sort of like how Knights of the Old Republic II is Kreia's story told through the eyes of your character. Your character still went around doing heroic or evil things in Fallout 3's side quests, but he or she wasn't particularly mysterious (mostly thanks to Three-Dog), nor all that relevant to the main story of the game.
Yeah but the problem is that is also the original idea behind just about every other video game ever made, were this unique to Fallout then I wouldn't have minded as much but the cliched character with no past feels like a hollow scapegoating on behalf of the writers and ruins my perception of the protagonist outright.
I disagree with you with your perspective, if anything I think that adding Dad and his quest only enhanced my own PC both as a character and as part of the story. While Dad might have been the originator of the journey, and has his own significant part of the tale told, it is the Wanderer's destiny/choice to actually see it through. In the end I think that the tale always was the Wanderer's, even if it was originated by his/her father, it added a new layer of depth to the story and a personal touch which I found much more interesting than being selected at random for no particular reason by the Overseer as a 19 year old to go out with no training nor any knowledge of the wasteland in order to blindly seek a water chip.
In many books and films we often see children take up the quests begun by their parents and make it their own. In sci-fi you can find examples from the Dune saga to Star Wars. The mysterious stranger moniker isn't original nor in any way all that interesting to me, in fact quite the opposite; I find such characters hollow, paper thin shadows who only serve to do things in the story as opposed to being a part of it.
I found the Wanderer's journey very much relevant to the main story of the game. But that's just me

Double edged sword...This is the guy that makes the best RPG hero; He has no past, no family, no ties, no friends... Nothing to lose and no one to leave behind ~But its also not much of a role.
Notice that Baldur's Gate gives you a past, and a foster father, and a friend... but kills the father, cuts off your past (Candle Keep), and the friend comes with you. In Dungeon Siege (IRRC), everything you have gets killed or burned up ~so the Farmer becomes the man with no family, no ties, no friends... Nothing to lose and no one to leave behind.
That's what I mean, these characters have a past and people tied to it and make it much more interesting for me as a player to assume the role they portray. They have something at stake within the story and the adventure, they might nbe motivated by many factors from revenge, to desperation, to sacrifice, to loyalty, to love or friendship; this makes the protagonist infinately more interesting for me because I want to see his/her journey through all the more.
Addtionally, I love lore. Not just ingame lore about any specific world, but lore involving anything created for the game which only makes it seem more vibrant and rich. I want to know about the lore of the town where I grew up in, the lore behind the PC's family, the lore of the world, the history of events which shaped things to get to the way they are now, the friends and relationships the PC had before the journey and during it and how all of these things tie into the main arc, and sub-arcs, of the story.
They did this in both Fallout 1 & 2. You could find combat trainers that could help you ~unless you already knew more than they did.
I remember a few of those yeah. I think something along those lines, with restrictions as to not abuse and max out everything, might be a more immersive way to learn certain skills which would otherwise would be unrealistic within the starting areas of a vault or tribal village, using the games' starting points as an illustration.
What? How is non-existence stale? Do you actually even think about your character's parents when playing Fallout 1/2? I sure as heck don't, so I don't see how that could get stale. Including the character's parents just for the heck of it every single time would more likely to get stale than simply not including them. Dead I can agree with since there are way too many RPGs that start out with "village destroyed, parents murdered, vow to avenge deaths" introductions.
As I mentioned above very much yes!
I absolutely wonder about my PC's origins and the people tied to it. For me it can get stale because there is no sense of history, no sense of depth when characters are devoid of any past; they are just shells or ideas of what a character is supposed to represent but not a character proper.
I'm not suggesting including a full family history in every game, every time. But when it comes to RPGs where characters and story can be extended beyond the surface depth of run and gun Agent 23 before the alien clone army can detonate the nuke in Sector 7, lets just say that I hold character development here to much higher standards.