There are a number of stories using this plot. For instance, the time traveler in a suicide mission murders Hitler in 1925. His co-conspirators in the present check it up and notice immediatly that he failed since history didn’t change : Ernst Thalmann somehow survived and led Communist Germany to WWII. They deduce from this that the past can’t be modified.
You’re definitely right about the infinite aspect. I’d notate differently, the new timeline is created as you arrive in the past, not when you do something “significant”. There is no godlike arbiter of significance: once you arrive, there are atoms there that weren’t before. You could arrive at the bottom of the ocean, promptly die and decompose, but forever there will be trace details that are different because you were there, thus a different timeline. You’ll still be born and still travel back in time and create a new timeline, infinitely. It does seem like a bit of a waste of whole universes, but then, any multiverse theory does that. One infinity, two infinity … no difference!
By this theory, once bifurcated, two timelines never rejoin. Perhaps if black holes destroyed information (which currently the belief is they do not; they obey the 2nd law of thermodynamics), two timelines could end up being identical. Does that mean there are two identical timelines or have they joined into one? Is there a difference?
There also isn’t a problem with those infinite second time travelers, though it was a great thing to consider. Let me set that up. Traveler A jumps back and promptly dies, making no noticeable difference in human affairs of the past, creating an infinite number of timelines. In each of those infinite timelines, traveler B jumps back to a point before A’s arrival in the past. They all “arrive” at the same world, but the arrival of each creates a new timeline, with just one traveler arriving.
That’s the fun thing about the multiverse. You can use up worlds to your heart’s content and never run out! (I admit I’m not a big fan of the multiverse concept, though.)
The only thing I can think of is that “now” actually isn’t any more or less important except for that is how we perceive the universe. Sort of like how the Earth appears flat when you’re standing on it. The structure of time and space might appear very different if we could perceive all events simultaneously like the Tralfamadorians from Kurt Vonnegut’s books.
I picture the timeline as a tree diagram. From any given point, the future diverges into a myriad of branches, depending on the choices made. From any “now,” you can move forward into many possible futures, but you can only move backward along a single path – the branch that led to your “now.” Once you arrive “there” (excuse me, “then”), your chances are slim to none of being able to return to the “now” that you started from, because of the infinite number of paths going in that direction.
Ever read James P. Hogan’s The Proteus Operation? One of my favorite time travel novels that uses this model.