I know a lot of the time paradox questions have focussed on "if the observers didn't exist, then september couldn't have interfered with walternate or have saved Peter in the lake" but I think there is another question I haven't seen addressed anywhere...
If the observers didn't exist, then how could Michael exist?
If the observers didn't exist, then September never existed and Michael never would have been created (built? cloned? ...?) and if Michael never existed, then he couldn't have gone to the future to be studied therefore preventing the observers from being created, therefore the obervers did get made and he would exist but then him going to the future would prevent the obervers from getting made and round and round.... major paradox.
the only way around it that I see it is what the observers allude to - that there are many possible timelines but only one that actually comes to pass (for lack of a better description). That the universe fundamentally shifted at the end of season 5 like it did at the end of season 3. That the whole 5 seasons of Fringe never happened and were replaced by yet another timeline (timelines if you count the main alternate universe) that was very similar but slightly different based on the lack of observers. That everything we saw kind of like a single timeloop that is then reset on it's "proper" path. (I wish I had a diagram to explain it better). So the observers existed but only in a single timeloop and didn't effect the ongoing flow of the "proper"/"main" timeline.
Like in some sci fi shows where time branches with every decision but not all branches are equal. That there is a "prime" timeline that is most important.
I like to think (as someone else suggested) that Peter receiving the white tulip was a trigger for him remembering the original events (just as Olivia's memories reverted to the season 1-3 memories in season 4) and that due to the Olivia's gifts, she too would have gained her memories of everything that happened.