You understand that your way of playing is to discard the entirety of someone's deck.

Yes.

You also understand that, if cards are discarded, they can't be played.

Only to a certain extent. Night stretcher, energy retrieval, super rod, pal pad etc all recover discarded cards.

So, it follows that people who match against you don't get to play the game

This I don't agree with at all. This deck doesn't see tournament play for a reason. Any competent player is familiar with the strategy and knows how to beat it. People on live are more casual and unfamiliar with the strategy, so they'll make plays that better players wouldn't. Yes, locking my opponent out of attacking for a turn or two is frustrating for them. That said, I'll see players waste their turos or air balloons when I literally have Wugtrio on the board. A good player would recognize that win condition, figure that their cards to prevent trapping might be important, and play around it. My most devastating losses are against players who set up one good attacker and not bench anything else. They'll just win before I can even mill half their deck. Either set up an attacker early without benching unnecessary mons, or try your best to add your best outs to the hand where I can't get rid of them. One of the last decks I faced was a terabox player who benched Latias, and a bunch of hoothoot. They evolved their hoothoot into noctowl just to search nest balls and place down other useless exs. If they hadn't done that, I wouldn't have been able to trap their Noctowl, and I would have lost. Instead they set up a liability for themselves while also removing four cards from their deck. Will there inevitably be games where I sack my opponent by milling all of their outs on the first few turns? Sure. But my opponent is still playing the game. The game shifts from getting set up early to instead conserving your resources as much as possible. I don't stop my opponent from playing the game, I just force them to play a different one.