When Link were first announced, many duelists said they would retire for good. A fair portion of them did, but there are also a lot of people who are fine them now. Whenever a new mechanic is introduced to the game, many react negatively. But the reaction to Links was exceptionally negative and with understandable reasons: sweeping changes, confusing rules, forcing decks to adopt them in order to utilize their own combos and threatening the viability of decks that couldn’t summon them easily.
However, I don’t think Links were the root cause. They were a symptom – not the disease. For players that left, it was the last straw after years of pre-existing frustrations.
After the XYZ era, players were a little jaded from the predictable formula of summoning two generic filler monsters to create a monster that actually mattered. They did not necessarily have a problem with XYZ’s, but they did not want a game centered around one dominant mechanic every few years. Then, Pendulums. At the time, they were seen as a drastic change that was confusing to players. Beyond that, Qliphorts were a terrible introduction to Pendulums. Of course, cards which were combined Spell/Monsters had potential for versatility and creativity in deck building, but the application just resulted in specific year-long archetypes with frequent Pendulum support having the advantage. The amount of power creep needed to compete against a type of card that could summon the same monsters over and over again each turn to repeatedly swarm and generate card advantage was immense. Links were only a consequence of all of this. It was a choice of this amount of power creep continuing or the game completely being yoked by a set of new rules. Regardless of how debatable the actual implementation of Links was, giving the game constant drug dose of power is eventually going to turn ugly because exponential growth eventually collapses.
There’s also a portion of Yugioh players that were around since 2002 and enjoyed the game for its nostalgia, but as the game drifted away from its fundamentals, players got less and less interested. 5-10 years ago, a lot of old school players were open to adapting their playstyle to Synchros and XYZ’s. During the years before Links, a portion of players played on-and-off or were slowly fading away from the game anyway. Many players who were once willing to devote a lot of time to the game when they were 16 now have marriage, kids, new hobbies and/or a demanding career. Much like the other rule changes, Links don’t take a brain surgeon to understand. Anyone can do it. For the players that quit, it’s not that they can’t adapt. It’s just that their ties to the game are much thinner than they were years ago and they don’t have as strong of an interest in the game to ride this whole new rollercoaster.