To clarify, I think a part of the problem is the sense in which the word ‘illusion’ is used. To experience something that doesn’t exist, and to experience something that doesn’t exist at a fundamental level of description are two very different things, and only the second is really amenable to physical description. The first, well, I don’t think it’s a sensible meaning of illusion to use in this context – after all, our experience of time is extremely uniform, almost all people experience in almost exactly the same way in almost all circumstances, contrary to other ‘illusory’ experiences, where typically only you believe that you are Napoleon, and such uniformity yields strong evidence of a systematic origin of the experience; however, conflation of the two leads to confusion.
Macroscopic phenomena, by and large, tend to be of the second kind. Think, for instance, of the wetness of water: there’s nothing in a fundamental molecular description that could be called ‘wetness’, nevertheless, the experience of wetness is fully explained by the molecular theory as a reaction of our somatosensory system to certain electrochemical properties of water. Or, think of the directed aspect of time: microscopic physical laws are typically time-reversible, on only on a statistical level of description does a preferred direction emerge, for the simple reason that a certain kind of evolution of the system is vastly more likely than another, simply for having many more possibilities to evolve that way. The directionality of time is illusory in the sense that it is due to our experience of the world in a ‘chunked’ way of macroscopic states consisting of a great many microscopic states (if we neglect certain microphysical processes that are manifestly time asymmetric, which we can to very good precision).
In fact, such directionlessness also emerges in certain occasions in the macroscopic world: consider a game of billards, or carom so we don’t have to worry about balls getting potted. Each collision (if not each shot) of balls with each other or with the rail is perfectly time symmetric; if presented with a video, you could not tell if it was played backwards or forwards. There already emerges a problem with predicting the future: which way is it? As time lacks its directionality in this context, ‘future’ has no coherent meaning. The problem gets only more severe the further down the rabbit hole you go.
So, if we would build a machine to observe the world in a microscopic way such that time was directionless in order to ‘predict the future’, then in that context, there would be no future to predict. Said pointedly, future only has a meaning (or at least, its usual meaning) in a context in which we can’t predict it – so changing that context can’t help us predict the future.