No, haven't read the whole thread, but will back track after initial comments.
My question is, in a world where such time travel has become common and ordinary, what are the consequences? For example, everyone who'll be famous for any reason will be known from their birth right through their life, even before they achieve whatever it is (for a real life example, think of when Prince Charles or Prince William were born). Criminals would know that they will get away with it, millionaires won't bother working hard to get there (because their names will be in a list of millionaires) and the register of marriages will tell everyone the name of their future spouses.
This is exactly why you see time travel dealt with the way it typically is, meaning it's either restricted to few devices or there's laws against messing up the past.
But what are the consequences? That's easy: the universe wouldn't exist. Really. More after the jump.
What else? What would happen to religions, in a world where the future history books tell you which religions are going to die out and which will become huge? If an asteroid causes worldwide destruction in the year N, won't everyone time travel away from that year to a future time when the effects of the destruction have faded? What else?
No, they'd time travel to prevent the asteroid hit. Because it would be easier. And humans are nothing if not lazy.
Over the course of all the galaxies, all the universes, all the dimensions proposed by real physicists, and the vast amount of time between the big bang and the possible heat death of the universe, anything that can or could happen, will. Somewhere, somehow, anything that is physically possible is not only possible, it passes probable, and becomes essentially mandatory. From weight of sheer numbers.
Okay, so therefore, if it were ever possible under any physics paradigm for time travel to exist, it will, and might already. And considering it's time travel, that means if it ever happens in the future, it still exists now as they could travel to now. My head hurts already. But, the point being, if time travel inevitably exists, then also inevitably someone's invented it and used it. In some dimension or pocket universe somewhere someone has gotten the hair-brained idea to go watch the big bang.
But, not only would our one time traveler have done so, just about anyone with access to the device and an ounce of curiosity would as well. Remember, weight of numbers. So you have tens, hundreds, thousands, millions? Billions? of time travelers taking a gander and the pop gun that started the race. Over all of time after the device is invented, all species, all planets with access to it, again, sheer numbers dictates that not only will someone do it, but a massive amount of beings are likely to do so.
Forget the doctor letting Rory's da dangle his feet out of the TARDIS and have a snack, watching the big bang would be like a stadium event. You'd have people hawking tickets and punters queued up round the block... you know what I mean. Now, the presence of the time traveling punters would interact with the bang itself. The energy released would interact with the matter of the devices and travelers themselves...
Which would mess up the distribution of stuff released from the big bang, causing those universes to evolve differently. Or exactly as they "were meant to." Point being, things would get messy. If any of a billions things didn't go just so, we wouldn't be here to talk about it. If you've got millions of punters having a go at the big bang, they're going to mess with the distribution of matter and energy in their universe altering it impossibly.
So... any universe where the physics make it possible for time travel to exist, it inevitably would exist... which would cause a temporal traffic jam just as inevitably thereby mucking about with the early universe which would make that universe go sideways in a hurry.
Thankfully our universe is here, as far as we can tell, therefore, time travel is impossible with our universe's physics.