I am a TCG judge, but there are also judges for the video game and Pokémon Go. I can only answer why the TCG has judges.

Sometimes, the rules present some ambiguity, so a judge is needed to resolve disputes. There are also niche edge cases which not all people are aware of (for example, you generally can't play a card that searches your deck if you have no cards in your deck, unless the card has other effects), so it's helpful to have a rules expert on hand.

Some tournaments have significant prizes on the line. I've reffed events where the total prize pool was hundreds of dollars. When that happens, inevitably, there are disputes and people make mistakes. Judges are there to enforce the tournament rules and serve as the official arbiters for disputes. Sometimes, people inadvertently break the rules, by playing cards they're not supposed to or by forgetting to perform a required action. When that happens, a judge steps in to resolve. And sometimes, disputes are just petty adults acting like children, like complaining that your opponent did not shuffle their deck throroughly enough (but sometimes we do observe actual children not shuffling their deck well enough, but they're children so we just go and shuffle for them)

Judges also deal with disciplinary problems too. For example, we have the ability to issue penalties to players for rules infractions or disqualify or ban them for being disruptive. These penalties are recorded on the Pokémon Company's player database and if a player gets kicked out of too many events (especially prestigious ones like a regional tournament, North America/European Internationals, or the world championship), they eventually may be prevented from attending events.

It's fortunately never happened at any event I've worked at, but an examples of some things that would get a player disqualified would be failing a deck legality check unless the player fixes it immediately, cursing excessively, annoying other players and refusing to stop when asked, being caught cheating, wearing inappropriate clothing/not exercising good personal hygiene, or drinking alcohol or being drunk/high.

You still need someone to organize the tournament and generate pairings. You need someone who knows the rules about how to handle game glitches and know how to recognize if someone is triggering a glitch intentionally. The judge also needs to monitor player behavior outside of the game (When does a player celebration cross into taunting? When does a player reaction count as violent or threatening?)

For example this disqualification for shaking the game table: https://aftermath.site/pokemon-go-firestar73-disqualified-statement-community-outrage/

It’s nice to have an expert on the game readily available. Any card game is going to have strange interactions that would take a long time to debate between players. A neutral 3rd party being able to have the final say and keep the game moving. I’d also imagine due to there being prize money on the line you need someone to watch out for cheaters and keep score.

It's quite common in trading card games for there to be disagreements between players on how different cards interact with each other during gameplay. Judges are just rules experts with the ability to mediate those situations.