The advantages are that it's much quicker. You usually skip a longer line but even if not, your time at the desk is usually significantly shorter because your folder with your name on will be there ready and waiting with keys, room charging, dashboard parking thingy sitting there pre-created.
I've also come away with the impression that they assume if you're savvy enough to do online check in, you've either been onsite before or you at least have a basic understanding of the different parks and how it all works etc so they don't talk you through all the individual pieces of paper in your folder ("these show you the park hours, these are EMH days, these are your park maps...") in so much detail.
On the flip side, I don't think there are any dis-advantages to online check-in. If you *really* don't like your room allocation which is most people's worry you can make still make a request with the CM at the desk anyhow and if something else is available they can move you and re-print the keys. If nothing is available then that would be the situation even if you were checking in the normal fashion.
Like you say, people can make some very specific requests but there's zero guarantee you'll receive them either way of checking in. Except for 1 occasion at Boardwalk (everyone hates those long corridors

) I've always received my - granted minimal - requests when doing online check-in.