Why are anticausal systems even defined? I guess the same question is usually asked for complex numbers too, but the fact is that complex numbers are used all the time practically. However, at least on a quick google search, I couldn't find any applications of anticausal systems. So why define it in the first place?
Of course they don't exist. But we can stop time and use systems that would be non-causal if we hadn't stopped time. Stop time? Yes, just store your data and work offline / non-realtime. Or work on data that are not temporal but something else, for instance spatial. Of course, non-causal is a misnomer in that case, but the term is still used, in analogy with temporal signals and systems.

One common "non-causal" system that is used in offline mode is filtering followed by reversed filtering using IIR filters. This is done in order to eliminate phase distortions introduced by the conventional (causal/realtime) use of the filter. See this answer for the details.