Here's the problem with the whole "Peter never existed and it could have changed things" scenario: Peter never existing would have had NO EFFECT on William Bell's health, or his living or dying as a result of his poor health.
With Peter being "erased", only things that HE AFFECTED - no matter how small - would have changed. Everything else would have been the same. William Bell died in Season 3. There is NO WAY they can reach back to Season 1, then Season 3, and somehow "change the facts" that he *didn't* die, and is somehow still alive. Just. Not. Possible.
Yes, the writers screwed up, IMO. Big Time.
I still don't like the whole Observer Occupation storyline. The technology for them to see the past, present, and future all at once is too great. As someone else postulated, perhaps only those who were sent back as "observers" had it. That still means they have the technology - and thus, they would KEEP it, and keep USING it. It's a huge weapon, especially when they know there is a rebel faction amongst the humans, which they clearly were not wanting (let's assume that based on the description of the 2015 invasion where "...the Observers went door-to-door, pulling people out into the street, killing them." HOW did they know who to kill, and who to let live? By using the same technology they apparently lost and no longer have, for some strange reason.)
It's like the writers just took everything they'd already written, threw it out the window, and said "gee, I hope nobody notices this."
Just like with "injecting Walter with a piece of his liquified brain, and it magically re-absorbing and letting him access those areas that were removed." Seriously, I have no problem suspending belief to enjoy a show, but they injected him, and mere SECONDS later, he's suddenly back to his old self? Everything just magically worked, easy-peasy, just like that? *THAT*, by itself, was a jump-the-shark moment.
Of course, I realize that the writers are trying to stuff as much as they can into the show before it's done. If there is no Season 5, they want the end of Season 4 to be the end-game. But in doing so, they may have made the possibility of no Season 5 a self-fulfilling prophecy.