Okay, how about this.
You’re walking up to an intersection at which there is no stoplight, but there are stop signs in all four directions. As you get to the intersection, you see a car barreling down the street you intend to cross. The car is clearly going at least 20 mph over the speed limit, far too fast to be able to stop in time. You then look at the stop sign and, as is your legal right, proceed into the intersection…where you get creamed by the car that had intended to run the stop sign in the first place.
Legally, you’re 100% right, and the car is 100% at fault. Realistically, you’re an idiot. A dead idiot.
Now, obviously, the situation described in the OP is nowhere near as clear-cut as the above example. Nonetheless, just as the hypothetical stop sign runner’s intentions were clear, so too can we guess at the potential motives of a person waiting to pull out onto a street. Yes, it is the driver’s responsibility to ensure that the way is clear before proceeding. Sometimes, though – and quite often, if the personal experiences you’re all relating are any indication – that just doesn’t happen. So, for one’s own safety, it might well be prudent to walk behind the lead car. The main advantage of this is that while the lead driver may well only be paying attention to the traffic flowing from his/her left, one can assume that the driver of the second car is looking straight ahead, watching the lead car in anticipation of it getting out of the way. Even supposing our two drivers are equally single-minded, the second is far more likely to notice you incidentally as you cross his path. Furthermore, it’s a pretty safe assumption that the second driver isn’t going anywhere at least until the lead car moves, giving you a convenient little window in which to do your street crossin’ thang.
None of this absolves either driver from any responsibility, nor does it strip the pedestrian of any rights. It’s simply a good idea based on what we know to be true – drivers don’t always pay attention to everything they should. I think that, rather than a change in current right-of-way procedures, is what the OP was suggesting.
Of course, I could be wrong; maybe Anaamika just enjoys mowing down random street-crossers. In which case, may I just point out that it’s ever so much easier if you never stop in the first place. Not that I’d know… 