[simonh]

Larry Niven speculated that if time machines were possible, time travellers continually going into the past would change the circumstances that lead to them inventing their time machines and using them, resulting in an unstable timeline. The only steady state for this timeline would be one in which no time machine was ever invented.

So we may well live in a universe in which time travel is possible, and time travellers from alternate future timelines may even have arrived in it in the past (or may arrive in it in the future from more distant futures), but the 'final value' of the timeline would exclude the events that lead to their actual invention.