The need for wood is going to be modest, and mostly in the early game, with resin acting as a modest wood sink until you unlock other sources of coal or explosives.

I was hoping for another use, but I can't really find anything. but I could be wrong. (Technically, you could manually plant wooden canes to get more out of them, because you can plant them much closer together, but this is a game about automation.)

Early game, it's no good as a fuel, it's outperformed by Cuttlepop, which grows on the same terrain:
Each Water Cane nets 2 (3 -1 seed) * 2MJ / 2.25m (2 minutes and 15 seconds) = 1.8 MJ / m
Each Cuttlepop nets 3 (4 -1 seed) * 3MJ / 4m = 2.25MJ / m

Mid game, you get some use out of it with resin and mulch, , but you'll be rapidly moving on to coal synthesis, which opens the door for easier explosives production.

Late game, it's mostly only good for grenades and mulch.

In short, I'd suggest some kind of alternative recipe that uses wood to produce something efficiently on Gleba(like Carbon) and perhaps raising the fuel value to make cane farming a better value proposition.