Makes sense to chop down trees in town. The second town I spent time in had an organised orchard. But when Godzilla smashed a bunch of buildings (bloody literally walked down a street stomping everything), people basically had no choice but to chop everything down to make wood for repairs. No time to find trees outside.
There is probably a nice sweet spot in terms of farming that you'll figure out eventually. 5 food needed for a sapling to grow another tree. So you should harvest a minimum of 5 fruit from a tree before chopping it down, otherwise it's costing you more than its returning.
An orchard can indeed make an excellent emergency wood supply, but I'd say that in general, it's better to just let them grow an abundant supply of easily harvested food, and get your wood from the islands where it appears fully formed and ready to chop. Remember that sacrificing your lovely orchard also means having to rebuild it afterwards, which is a lot of work on its own.
Regarding monster attacks, your town
should be defended well enough that they typically don't breach the border in the first place. Godzilla in particular you want to drop just outside the edge of town, so it's easy to go out and harvest them, but you don't have their corpse clogging up town square for a couple of days. You shouldn't need to do any repairs at all except after the bigger attacks. Think about Walking Dead. Mostly what keeps them safe is a large wall that can't be damaged by normal means. We need the same.
Obviously, shit happens, and you gotta do what you gotta do to get by, but I don't think growing your own wood should really be the
plan unless your town ends up growing so large that the islands simply don't spawn enough to meet your daily construction and maintenance requirements. Even when you do reach that stage, it may be more efficient to chop saplings as soon as they mature, before they even fruit, and just set up a "feeder orchard" of appropriate size to do nothing but produce apples for saplings. That'll mostly depend on timing, but it seems like the saplings mature comparatively quickly, but take a while to produce even five apples.
Let's say it takes a tree 20 minutes to mature, and 60 minutes to grow five apples. If you let the tree grow long enough to produce "its own" sapling, that cycle produces three pieces of wood every 80 minutes. Multiply that by a dozen trees, and you're producing 27 wood an hour. Not too shabby.
But, an already mature tree can produce enough fruit to create a new sapling every hour. If we dedicate three trees to sapling production, that will produce three saplings an hour, or one every 20 minutes, which is how often we want to chop them down. That means that just three adult trees can actually produce 9 wood per hour, so with a dozen dedicated to that, you'll actually be producing 36 wood per hour, 33% more.