Maybe a Barbarian Woodcutting method that also gives Strength similar to how Barbarian Fishing gives both Agility and Strength as well as Fishing xp. That said it would probably be a token amount and Strength is already a vastly faster and easier skill to train than Woodcutting so it doesn't seem necessary.
#Woodcutting gives Strength XP
blissful elm
queen sand
Id possibly be okay with a barbarian woodcutting method as mentioned above but str while woodcutting I give a strong downvote too, some people dont want str xp and I see no reason to combine the skills
digital turtle
My reasoning was because the labor builds strength naturally. I've learned that cutting a tree with a fireman's axe is extraneous, but also those who make it their profession are made bulkier from the process.
queen sand
I mean I understand your reasoning, but a lot of skills use strength, all parts of fishing basically use strength, mining uses strength, archery uses strength, attack uses strength, agility uses strength, construction uses strength, smithing too. Let skillers keep their level 3, I dont think it really benefits anything to change it