If you're upholding PokeMon as proof that you can still tell rich stories with a variable lead character, you're grasping at straws. The most interesting story told within the PokeMon universe only happened once Twitch started controlling it.
Mass Effect is unique, mainly because you set up your character's backstory as a part of the character creation process. That's how you have a legend, and it's what they base the character relationships off of (when one is presumed to have met you prior to the game's beginning). For a game as sprawling and focused on relationships as ME, it works. They made the sort of game that allowed them to write complex, interesting plots that worked with different spins on the MC. Zelda is not going to do that. I don't want that to be Zelda.
This is a simple matter of storytelling. If I'm writing a plot for a game, and I know exactly who the main character is - all their traits, all their characteristics - it allows me to treat it like any other medium. I can write a huge sprawling narrative that happens both before and after the game itself. Characters who interact with the lead can have a history, because they've interacted and I can craft stories about who they were - and why they are who they are now.
But let's say I can change the name of the character. No huge deal. The name doesn't mean much. Sure, if the character is some universe-breaking thing, it would theoretically be a part of their history - but at that point, it's a fault on the player and not my issue.
Now let's say I can change their gender. Depending on the world I'm trying to write, that might have massive consequences. Depending on that variable, they may have interacted with a certain character in a different way - left that interaction with different impressions of each other.
Why not change race as well? Now I've got to wonder about that. If Link can have a different skin color, does that alter how he's seen in his community? Are individuals more or less willing to trust him?
And sure, you may say "Just don't write characters that treat people differently based on those variables". But that's creatively stifling. If I'm writing a game where the player can be any gender or race and ensure that has zero influence on the story - that means I'm limited to writing stories where gender & race are non-issues.
Sure. Some of these concepts may not come up all that often in a Zelda game. But there are artists who craft these worlds, and have detailed visions to the lore & mystery behind them. It's what makes this franchise so beloved - the rich nature of the world. Introducing a customizable player character puts a reign on that creativity. And I want to avoid that at all costs.
If you're implying that Zelda somehow has a rich narrative, or is somehow above Pokemon or any other game then you've completely lost me. Seems like it's perfectly comparable to Pokemon. Like what do you have, prophecy, legends, boys goes on adventure, beats the bad guy. Silver probably has a deeper backstory than anyone in a Zelda game anyway what with the child neglect, revenge and reconciliation.
That Mass Effect back story is hardly important, just as whatever characters who have history with Link usually aren't. The only time it's brought up in Mass Effect is in throwaway dialog and one or two side quests.
What are Links characteristics? He's silent and allegedly always brave. That's such a difficult character to construct a narrative in one's head around. Look at OoT, the only person who has history with Link is Saria and the Kokiri who are forgotten about in a half hour. So how important is this history again?
How does someone playing as a girl affect you then? It'll be the same narrative, people are still going to react to you the same way, you're still going to save the world, you're still going to make up whatever personality you want in your head. If people choosing a name doesn't affect you, them choosing a gender shouldn't either cause you'll be in your own adventure like you already are.
You say that changing the gender might have serious consequences...how? So Saria doesn't have a crush on you and Ruto doesn't want to marry you? Or maybe they still do? How is this a serious consequence? These are one note characters like most Zelda characters.
Well why not have an option to change the race? Why not have darker skin? I'm assuming you're referring to that. It's not as if they're writing a story where being a white male has consequences in their games right now. Unless you mean change to zora, or gerudo or something. Then yeah, it would have to change the story. But that's more of a species change.
I dont know, I dont really see Zelda as a bastion of sociopolitical narratives. This is a series with female kid pirates like Tetra and where everyone acts like this is normal. This is just a story of hero going on an adventure, bad guy wants to rule the world, hero saves the day. To me, playing as girl doesn't hurt the lore or the world at all because gender hasn't ever been important to the narrative in the series, nor has a character select screen been any more atmosphere destroying than a file and name select screen. I don't know why being a little more inclusive would hurt.