I live just up the road Glenn, and we have 14 acres. I'm pretty good with my Husky, but I don't head out without a few shims and an ax. Pinched chain, maybe help a tree fall the way you want. Just can't see a tree cutter who doesn't carry an ax and wedges.
The topic is the whether an axe, in the OP's language, is "essential"
for canoe trips of the average kind that the members here may take. The topic is
not how we heat our homes in winter or clear our back acreage.
An axe is not essential nor even desirable for any canoe trip I have ever taken. I don't go into remote forest wilderness for weeks at a time and have
never had any need to chop anything with an axe. Because I canoe in mostly warmer times and climes, I rarely even make a fire. Too lazy. When I do make fires, I have never needed anything more than a knife and a folding saw. Natives who live in rain forests around the world most commonly use machetes to to clear land and split wood. The machete is a tool that is very undervalued if not unknown by canoeists, and I would recommend it a more versatile and safer tool than an axe for splitting kindling or clearing brushy trails on a canoe trip for those who, unlike me, do such things.
Though irrelevant, what we use to clear land at home depends on what kinds of implements one happens happen to like. I agree that you can take down a tree with an axe and wedges, as we used to do with big pines in Maine 60 years ago, but I have done everything I need to do over the past 20 years with a chain saw, pruning saw and machete. (And a bush hog on my tractor.) I have hired professional tree surgeons to fell big trees near my house and they did everything with a chainsaw. I've also never seen a road crew in Connecticut taking down trees and limbs with anything other than a chainsaw, including a six foot diameter sycamore across the street from me.
Whatever one's favorite tree felling implement, which can vary from person to person, I don't see cutting big trees to be something related to canoe trips.
I don't care if some posters here have a love affair with axes and want to talk about them in comparative, historical and photographic detail. I like non-canoeing threads.
I only jumped in to get back to the OP's specific
canoeing topic: whether an axe is an
essential piece of equipment for the average range of canoe trips, especially those trips that newbie readers may be contemplating. My answer, which is based on more than 60 years of warmer weather paddling all over North America by myself (solo), with others, and with various groups such as the Sierra Club, Appalachian Mountain Club and Adirondack Mountain Club, is a definitive
NO.
Very, very little is "essential" for a satisfying canoe trip -- including, for example, lightweight carbon fiber canoes and paddles, electronic gadgets and gizmos, or booze. JMO.