If you do decide to keep the wood, here's a thread where I asked about it a couple of years ago--people had suggestions on how to finish the wood for a bathroom use: https://www.houzz.com/discussions/6139569/wood-floor-in-bathrooms-moisture-concerns-other-issues (Worth noting that there was cost entailed in that option too, though not as much as the replacement.)

In the end our decision was driven by my partner having a lot of concerns about wood in a wet area and trying to stay with the aesthetic of our 1915 house, since the original bathroom had tile floors when built and when we eventually renovate that one, we plan to do a period-appropriate tile floor. Of course the bathrooms don't necessarily need to match but I liked having them similar in style/feel. I am also laughing about how I thought our kids wouldn't use the new bathroom...that happens far more frequently than I'd like, and they are definitely not great about containing water, even with a shower door! One option we didn't consider that might be one to think about is to do a tile inlay in the wood right outside the shower so that the floor immediately adjacent to the shower entry is tile but the rest is wood. That might be tricky wrt height of flooring, though--our tile is slightly higher than the wood.