If I counted all the time I spent browsing the Terraria wiki as part of playing the game, I would probably be almost done by now. I'm not at all sure how this game could possibly exist without the internet. There's just so much stuff, and it's not obvious how it's connected.
Perhaps, in this hypothetical world of complex 2D games, but no internet, people would just explore Terraria naively, and stumble upon its various secrets in the normal progression of time. Perhaps they would have notebooks full of reminders and theories, and they would flip through them whenever they found a new mineral or encountered a new monster. Progress in this world would be half inspiration and half chance. You would be surprised by the Eye of Cthulu fight and then start new characters just to see if you could work out the triggering conditions. Terraria would be a deep and mysterious thing, and your hard-won knowledge would be the result of obsessive observation and repetition (or maybe you'd just give up really easily).
Because I have access to the wiki, I was not surprised by my first boss battle. In fact, I deliberately took steps to move it along. I'd gathered my various equipment, delving deep into the ice caverns in search of platinum and finding an improved version of my magic boomerang along the way, and I was starting to get a little antsy for something to use my superior equipment on. I remembered that there were bosses, but didn't see any obvious way to find one, so I looked it up and discovered that the Eye of Cthulu spawns randomly at night once you find five life crystals, so I searched for another life crystal, waited until nightfall and got lucky.
Would I have even bothered to try if it weren't for the wiki? I can't say for sure. I like collecting things and upgrading my equipment. I would have enjoyed exploration, even if there was nothing particularly special at the end. I don't think I'd have bothered trying to trigger a boss, though. I like solving problems, not mysteries. Give me a chasm to cross or a tower to build and I am on that like no one's business. But if I don't even know for sure that there is an endpoint to the challenge, if it's possible that I'll just spin my wheels forever chasing a dead-end lead, that it kills my enthusiasm quick.
Or maybe not. I do like being systematic and poking my nose into every available corner, so it's possible that the solutions to these mysteries would come inevitably with time. I don't think I'd like to be surprised by the Eye of Cthulu, but I think I'd probably get over it so long as it didn't wreck my stuff.
I guess I'll never know now. Is this a loss on my part? Is Terraria meant to be played blind? Am I missing out on a unique experience by not simply taking things as they come? I don't think so. The tutorial is pretty weak, and I'm not at all sure how you're supposed to figure out the crafting system without outside help (seriously, it's not just combining materials, you have to have those materials while in the proximity of the right crafting station, which is fine if you get it, but easy to screw up if you don't).
In the end, I don't know if I'd call Terraria's (really the whole survival-crafting genre's) reliance on the wiki to be a strength or a weakness. On the one hand, it allows the game to be much more complex than it otherwise might be. A lot of the cognitive load for all these recipes and varieties of equipment are offloaded onto a more reference-friendly platform. On the other hand, it means the game is not self-contained. Which raises the question - in assessing the quality of a game, how much should supplementary material count? This is a serious issue in criticism, what with the "death of the author" and all.
I don't really have the expertise to come down on one side or another. I will, however, say that I enjoy playing Terraria and I don't mind consulting the wiki. It's not a decisive argument, but it doesn't have to be. I can't really play the hypothetical version of the game, so what does it matter whether it's better or worse?