So first of all, cores are *not* rare. Just visit a handful of chambers and you're set for a while.

Second, I used to think that mining copper really sucked, but in fact it's really how much copper is necessary that is annoying (the 2C + 1T -> 1B ratio is dumb). Mining copper is actually really cool. I dig all around the deposit, all the way to the floor and try to make it explode. It's fun, you get a ton of stones that I keep for iron age and then it's pretty quick to gather a lot of copper.

As I mine copper, I also fight monsters in the black forest that give me resources, I cut trees that are in the way, I collect shrooms and BB when going back to my base. I like hoarding materials for later in the game.

I find collecting iron more annoying. You can end up in gigantic swamps that have no crypts. You can finally find a crypt just to see that it only has 2 rooms. You need way more iron than copper to build stuff.