This is a complicated topic with a lot of factors. While I've never written a full design for it, I have given a lot of thought to this problem. It's probably a topic which in and of itself is worth a whole livestream to discuss, but I'll try to do a quick answer on a couple of points.
The simplest is that it's hard to do much with Woodcutting without also updating Fletching and Construction. This isn't insurmountable, and something like the core mechanics of Woodcutting don't inherently depend on Fletching being different, but anything more complex like new woods (which are needed really) or new reasons to train the skill would do so. Nevertheless the best angle I can see for chipping away at this problem is to start small and fix WC first.
On the other hand, any changes to the core mechanics of the skill do wreak havoc with the absolute ton of existing mechanics in the game. Totally revising the woodcutting mechanics is actually fairly straightforward - the initial M&S beta only took us about a month to put together. The other 18 months of the project were updating 20 years of minigames, rewards and other content that didn't work with different mechanics.
Making this more complicated, at a thematic level woodcutting is just sort of awkward - making a simple change that trees simply don't deplete would, to my knowledge, be fairly easy as a "hack" solution to the skill, but it's also not really the biggest problem. The idea that trees lose wood as you gain wood is so fundamental to the thematic fantasy of the skill that it's genuinely hard to solve both at the solo level and at the group level. I don't believe it's unsolvable - almost nothing is - but it is difficult.
On the topic of hatchets, it's been a while since I looked into this for M&S so I may be misremembering, but to my knowledge the problem is that the way the core WC mechanics work don't really allow for better hatchets, at least not without something clunky going on somewhere. Hatchets work on a delay system - the number of ticks between swings is higher for lower tier hatchets. The dragon hatchet has the fastest possible swing speed (1). The handful of better hatchets than this effectively have special bonuses on them that do something in addition to having the fastest possible swing speed. However, tiering this up further requires better and better bonuses, and this scales awkwardly when looking at how quickly you can chop lower level trees, resulting in a potential balancing nightmare.
On M&S we solved this exact problem with the hardness and penetration system - about half the benefit of using a higher tier pick only applies to higher tier ores, so you don't mine lower level ore massively faster than your current tier. This could be applied to WC with some non-trivial work, but because WC isn't currently tiered properly, it would be confusing and unintuitive in execution.
My opinion is that the next best step for WCing is to pick whatever turns out to be the easiest of these issues to fix in isolation and fix it in a way that allows for the next easiest to be fixed in future, and so on. Whether we can do that in part depends on the community's tolerance for medium sixed fixes as content, which is something I want to experiment with in the future.