Maybe you could, but the whole point of opening up the cart is to re-center the atty, if it needs it, and to have a visual cue so you don't overfill the carts. Prying the cap off the first time takes the longest - after that I can go from topping off a cart to vaping all day in less that 2 minutes... It really doesn't take that much time or effort once you know what you are doing.
On a side note, I keep all of my rubber O-rings and mouthpieces just in case I break or lose one. The carts will die after a while, but the spare parts do come in handy!
Everything in this post quoted above is absolutely correct. It's wise to recenter the atty, even on new cartomizers..but that's up to the individual user's comfort level of course.
It's wise to take off the mouth piece unless you feel confident you could fill a bucket with a garden hose at 30 feet in the bottom of a cave in absolute darkness.
Once you've removed the mouthpiece that first time, the hard part is over, particularly if you plan ahead and dont put it back on with a mallet. If you just mash it in with your thumb, leaving a teenie bit of rim, you can pick it out with that same thumb nail (as seen in the video) with relative ease.
Always save your leftover parts! Those mouthpiece caps and silicone 0 rings are great when you lose or damage one. Clean out an old coffee can or something, you'll thank me later (shameless ripped off of Monk)
And finally, once you get the hang of it and learn how far in to mash your caps so you can again remove them with ease, 2 minutes is about right for a non rushed refill. It's really really easy once you get the hang of it.
Remember if you *really* hose your refilling job and drastically overfill, you *can* blow through the mouth end to remove juice...but use sharp/abrupt/short blows (like when shooting a blowgun) because if you follow through, you'll empty the cart totally in one blow..no kidding. Also remember to follow that puff with a sharp blow through the battery end to send the juice you just sent to the bottom (away from the atty) back toward the mouthpiece end.