There's a difference between a woodsman's axe, and a war axe. And I'm doing all the book-keeping in relation to our hirelings, so there shouldn't be any forgetting about that.
There's also a difference between a standard claw hammer and a Light Hammer, but there is nobody in the world who is going to get me to agree the claw hammer should do less than 1d4 damage and crit on 20x2, when a wooden Club does 1d6 and crits 20x2 and Unarmed is d3 / 20x2. Similarly, a Hand Axe is d6 / 20x3 and I don't see why it can't do the same wood-chopping work that a hatchet can do.
Finally, let's look at damage vs. hardness. Wood is Hard 5, HP 10/inch. Your Hand Axe is only going to damage the wood 1 hit in 6, and when it does there'll only be 1 damage. Which means it takes 60 rounds (6 minutes) to chop through 1 inch of wood with a hatchet. A Battle Axe does d8, meaning on average every 8 hits will deal 6 damage, meaning you need about 13-14 rounds (about 1.4 minutes) to chop through the same inch of wood. Attack roll doesn't matter because the sailor can just spend the full round action to set himself and whack the inanimate object with a single attack per round for a melee auto-hit.
Of course, you make exactly the same progress chopping down a tree with a battle axe as you do with a flail.
And a camel (bite d4+2) can chew through a tree pretty quickly if it were so inclined, causing 1 hp per 4 rounds, or 40 rounds (4 min) per inch. A wolf (bite d6+1) does 3 hp per 6 rounds, taking about 20 rounds (2 min) per inch.
Let's use the wolf example, and say the Three Little Pigs have a cottage made of wood. The cottage is 20' on a side, and the walls are 6 inches thick. The wolf begins chewing at a corner and continues around until he finishes, causing the house to plop down at some point, whereupon he continues going around again. Here we wonder what size of an area of wall counts as a single object: one door is probably a good answer, let's say 6.8' x 3.1' which is a standard door today: about 21 sq. ft.
Let's also assume a cottage with 10' high walls and a 45 degree roof peak. The walls are (20x10x4) 800 sq. ft. area (this house has no windows and let's say the pigs installed a 6" thick door due to paranoia about wolves). That means a wolf tears apart the entire walls of the house in (800 / 21 x 2 minutes per section x 6 inches thickness) 457 minutes (7.6 hours).
The triangle of the roof side is 20' across, but the center is 20' high because of the roof peak, giving the side an area of 400 sq. ft (x2 sides). The two top panels are 20' across side to side because they match the length of the wall, but up and down the hypotenuse of the side triangle (about 14 because the other two sides are 10) makes it (14 x 10) 140 sq. ft. (x2 sides). The roof in total is 1,080 sq. ft., and if we assume it's also 6" thick (man, these pigs) this will take our wolf 617 minutes (10.28 hours) to rip apart.
Of course, the house probably doesn't have a 6" thick roof. If we assume a 4" thick roof, we're down to 411 minutes (6.8 hours) for the roof.
That's pretty much 15 hours for a single wolf to destroy a 400 sq. ft. building down to shattered fragments and kindling, or 8 hours to knock it completely over.
And the wolf would bite through a Strong Door in 4 minutes, so basically what I'm saying is in 3E your babies are already devoured.
And, of course, if you take an inch-thick paper panel and punch it, you have a 66% chance of blasting the whole panel into smithereens. If you punch a glass block 5' x 5' x 1 foot thick it'll take you about a minute to destroy it completely. Unlike Minecraft you can't punch a tree down - unless you're a 1st level Monk.
General Sherman is the biggest tree in the world, at 79' diameter at breast-height. The Monk punching the tree will destroy a door-sized section 21' square and 1" deep every 6 minutes. It will take our intrepid 1st level Monk (79' x 12' x 6 mins) about 95 hours to punch a tunnel through it.
The area of a cross-section of the trunk is (((37.5' x 12") squared) x 3.14) about 636,000 sq. inches. The Monk destroys a 1" strip of that cross section, 38" across (door width), per 6 minutes - or, (38 / 6) 6.3 sq. in. per minute. So it takes about 100,001 minutes (1,682 hrs, or 210 days of 8-hour shifts) to chop it down. But because the Monk can't just saw a thin line, he is actually destroying 6.8' out of the trunk height of the tree.
So our Monk, at maximum, will spend his weekdays attacking the tree for about 10 months. His weekends are free to lay around in the huge pile of woody debris and apply ointment to his aching hands.
Best part, in my opinion: if the Monk grapples General Sherman, squeezing as hard as he can, he will roll opposed Grapple checks with the tree to see whether he can cause damage. (Tentacles cause bludgeoning damage, which affects objects, and I assume grappling is doing the same thing as tentacles). The tree has no bonuses except its size bonus, +16 (Colossal), but the 1st level Monk has, let us say, +1 from STR and +1 unarmed attack bonus. If the tree wins, the Monk slides off without causing damage.
Leap, splat, slide.
BUT if the tree rolls lower than the Monk, the Monk attaches to the tree and squeezes.
Leap, grab, stick, SQUEEZE!
This cannot occur if the tree rolls 7 or higher (30% chance of possibility) and cannot occur if the Monk rolls less than 16 (20% chance of possibility). But these must occur together! I don't know how to properly determine the probability of this, but eyeballing it tells me the Monk should be able to do it sometimes. Maybe 1 time in 3 multiplied by 5? 1 time in 15?
That's about 15 times the squeezing, meaning 157 months of weekdays (a bit over 13 years) for a 1st level Monk to hug the biggest tree in the world to death.
And of course, the tree will fall before you get all the way through it. How far do you have to chop through a tree to get it to fall? Certainly not 100%. But more than 50%? 66%? Anyway, a lot less than 13 years. Let's call it more than 7, less than 13.
TL;DR: 3E requires DM judgment.
But, uh, my point about battle axe = wood chopping axe still makes sense to me.