CCK philosophy has an excellent video that I think explains the usefulness of the idea well. Their other work is a mixed bag imo.

On topic, I think the main thing is that arborescent thinking is representational, it takes things as being exemplars of an ideal and judges them based on deviation from that ideal, while rhizomatic thinking attempts to judge things for what they are and how their unique traits can be best used. The example in the video is that a drum machine is at best a mediocre replacement for a drummer, which makes it mostly good as a glorified metronome when used in that capacity, but if you think of a drum machine not in terms of how it is and isn’t like a drummer, but what the drum machine is capable of irrespective of what a drummer can do, then suddenly you have a real instrument with unique capacities that a drummer doesn’t have instead of just an inferior drummer.

I think this idea has a lot of application even just in everyday life and I appreciate it mostly for that reason, though of course it can be applied to political theory and such as well.

Edit: I don’t like the common fetish of “decentralizing” everything, I don’t think communism actually makes sense when it’s fundamentally decentralized even though that seems to be the very highest ideal that some people espouse, but there are still applications of rhizomatic thinking even in a centralized system, partly because the overall system being centralized does not mean that every aspect of it is, and I would in fact argue that this fetishism of decentralization is itself representational thinking. Centralization and decentralization each have their own uses and we should evaluate them on that basis rather than dogmatically favoring one or the other.