Why does Peter Bishop still exist?

Walter & September's plan was to effectively change the future so that the Observers/Invaders never exist

Not quite though. Michael is still genetically advanced with mental functions well above any human, however unlike the Observers, he still has emotion too, as September reveals in The Boy Must Live:

He is an anomaly, but he's not less than them. He's more. At first, I thought his abilities were just empathic, but they developed into something greater.

I now know that his intellect functions on a level that neither you nor we are capable of understanding, but what's more important, he has the emotions, the compassion, the empathy. A hybrid.

Later, when September outlines his plan to Walter, he doesn't suggest they will prevent the creation of super-smart humans, just emotionless super-smart humans:

When scientists first decided to sacrifice human emotion to increase intelligence, that was the turning point in human evolution: 20th of February, 2167.

If we can send the boy into the future to that moment, he can demonstrate to those scientists a different kind of intelligence, an enlightenment that goes beyond knowledge or cognition to something greater, and when they see what he is, when they study him, they will realise all that he is: Living proof that they don't have to sacrifice emotion for intelligence, and they will never go down that path.

This suggests to me that they will then continue with their research to increase human intelligence, but in a way which allows them to keep their humanity. This could therefore mean that instead there will be a different race of Observers who may send scientists back in time to Observe us, which in turns repeats the chain of events which lead up to Peter in the alternate universe.

The Fringe team may occasionally notice them, but this time they won't invade the past, because they have enough empathy to know that genocide is a bad thing.

Short answer: Because erasing all of the character relationships would have been a terrible and disappointing end to the series.

Long answer: Time loops work like that. If the Observers didn't exist, the Observer would never have come into the past and saved red Peter, the kid would never have gotten sent to the right point in time and Observers would have existed. No way to fix it other than for the writers to cut the cycle and say, alright, the Observers never existed, but their impact on the world when it came to Peter, Walter and Olivia's personal stories pre-invasion remains intact.