...Technically, Yu-Gi-Oh has been that way ever since the Envoy days of Invasion of Chaos.
Technically, it's been that way since the origin of competitive play, save for when you're trying to assemble your game-breaking draw/damage loop or combination of guaranteed 8000+ damage to your opponent's face instead. New cards just make it easier to do that sort of thing consistently.
Anyway, yeah, cards that like being sent to the graveyard are obviously a good counter to mill, but it's actually a bit of a mixed blessing, because with such a deck, you would want to be milling yourself too, and that - in turn - can lead to burning out your deck
really quickly. Now from my experiences with playing milling decks, I'm going to go ahead and suggest a different approach:
Extreme burn deck. Icha already mentioned Magical Explosion OTKO, which is certainly a formidable candidate for the job, but anything capable of hitting for large amounts of burn damage fast will make most conventional milling strategies cringe. Dedicated burn is a rare sight these days, and so it's unlikely that your opponent will have prepared to counter it. Chain Strike Burn should certainly be up to the task. It's a deck that attacks very rarely, so any walling efforts your opponent makes will basically be wasted while they also have to go through the trouble of flip summoning for whatever flip effects they want to activate, which means the effects will trigger slower. Chain Strike burn as a whole is also basically just one, big stream of hurt for your opponent, so it's not
as dependent on drawing specific cards to secure a win as most decks and will therefore also not be hurt as badly by random milling incidents (losing Chain Strike still stings, but it's not the end of the deck) and your opponent will usually have very few cards at hand that could deal with the threat of constantly being hit for big burn damage.
Also, though it's a bit old school, Skill Drain burn could also do the trick. Most worthwhile milling cards are effect monsters, so Skill Drain cripples them badly, and once you get a Wave-Motion Cannon down, winning will usually just be a stall game from thereon out, as dedicated mill can't afford much in the S/T destruction department.
Ceasefire is also a kick in the crotch for anything using flip monsters, and an easy fit into both strategies.
Venturing on to the obscure, Outstanding Dog Marron and Magical Blast are both cards that can keep you from decking out, basically forever. For added lulz, combine Marron with Mass Driver/Cannon Soldier and laugh as you chip your opponent's life points away bit by bit.
Also, Iron Wall burn could also work. It's a combo deck based on assembling Plaguespreader Zombie and Quillbolt Hedgehog in the graveyard and Imperial Iron Wall on the Field, then playing a Cannon Soldier or Mass Driver and going crazy. Plaguespreader is a tuner that can summon itself from the graveyard, and Quillbolt can summon itself from the graveyard if you control a tuner. Normally, both would be removed from play if they leave the field after summoning themselves, but with Iron Wall preventing that, you can keep sending your Quillbolt to the yard for Mass Driver/Cannon Soldier and pulling it back up as often as you like. End result: a trickle of tiny damage bits that keeps coming for precisely as long as you want it to. Losing your Iron Walls to the mill is a bit of a risk in this matchup, but there are ways to recur that card (Mask of Darkness comes to mind) and as far as the rest of the setup (the far trickier part) goes, your opponent's milling efforts will just be speeding the process up.
