Grappling is not predominant in modern MMA, and hasn't been for a decade or two, so the "matches seem to pivot on one competitor being forced against the cage...moving to the ground, and decided by definitive locks or holds" premise of the question is invalid. MMA matches are overwhelmingly striking contests.
Professional competitors in the modern era, particularly at the elite level, rely less on grappling than striking. Just look at the current champions and challengers, almost all pure strikers: Israel Adesanya, Paulo Costa, Dustin Poirier, Marlon Moraes, Amanda Nunes, Zhang Weili, Stipe Miocic...it's true of the last generation too: Anderson Silva, Mighty Mouse, Jose Aldo, Conor McGregor, Alexander Gustafson...the list goes on. Even incredible and decorated wrestlers like Daniel Cormier, Jon Jones, Yoel Romero, Henry Cejudo, and Justin Gaethje almost always use their wrestling solely to buttress their striking. Fighters like Khabib and Usman who prioritize wrestling are the exception, not the rule.
Closing the distance in order to grapple is one valid tactic of many, as we see with Aljamain Sterling's recent victory over Corey Sandhagen, or with the beat-you-anywhere versatility of fighters like Chris Weidman, Rose Namajunas, or GSP. But grappling is more commonly used as one tool of many, rather than as a primary strategy.
Good footwork can make it difficult for an opponent to take a defender to the ground
This is absolutely a major strategy used effectively at all levels of MMA. It works just fine in a cage, though it is true that a smaller cage makes it more difficult. But unless you expect to fight on a football field, fighting in an enclosed space is more analogous to self-defense than not. I note that in judo, it is a penalty to avoid engagement or to play over-defensively (called "negative judo"), as is stepping outside the contest area without immediately attacking or stepping back in.
In fact, the comparison with judo is instructive in a different way: it is easier to retreat than to engage. In this you are correct: if a competitor knows proper footwork and defensive grappling, then on an equal playing field, it is easier to avoid fighting (especially grappling) than to fight. That is why wrestling, BJJ, judo, sumo, boxing, kickboxing, MMA, and all other grappling and fighting sports have systems to force competitors to engage. In MMA, this imperative to engage doesn't much encourage grappling, since a fighter can choose a Robbie Lawler-style strategy to only strike, and if a shot is made or clinch occurs, to respond with defensive wrestling. You are right that against such an unwilling opponent, takedowns in the open are more difficult than against a cage.
Just like defensive footwork is a valid strategy, grappling itself is a valid strategy. It works because clinching up is a natural consequence of fighting, and because grappling is a major element of fighting. Relying on eye gouges and so on to defend against grappling is indicative that someone has decided they don't want to train grappling, and so invented reasons not to get good at it. It is a cultural or aesthetic choice, not a practical or strategic one. I also remind people making such claims that the superior grappler will also have those options available to them, and will be better able to apply or defend against such tactics. This is proven repeatedly when a newcomer takes an illegal grip on a skilled jiujitsiero, wrestler, or judoka -- in my experience, most will throw or pin you before or instead of calling out the rules violation.
