If you wanted to play through the story and nothing but the story, of course you could. Side quests, mining, harvesting, crafting and other such activities are entirely optional. For those who are invested in the game and the universe of Faria, however, may want to take a look at my favourite feature; "Relic Restoration"!
Now, you can catch a glimpse of the crafting process in the trailer. There are multiple crafter NPCs that cater to the specific fields of crafting and provided you have acquired the right instructions (crafting books) and ingredients, you can visit them to begin crafting to your heart's content!
One Nok in Port Faria in particular, however, specialises in relic restoration. It is the process of recreating relics from Faria's past. Each one has a hearty description that enriches Faria and The World's lore and many of them are actually connected. In fact, a rather beautiful "sub-story" of the game can be found within the relics, provided you can link them together well-enough.
Which ones are you most interested in reading about?