Something that already strikes me about audience response to Day's family in Last Twilight is the amount of anger and shaming language I'm seeing directed at them, and what I keep thinking is that Day is not Heart.
Sure, it may turn out that Ramon and Night have hidden what happened to Day because they're ashamed or don't know how to deal with it, that they're the ones who imposed the "abroad in the US" cover story, that despite seeing Aon use his cane when he comes over and Day lights up like he never does at any other time, they just haven't bothered to get Day a cane to help him maneuver the world. But we don't know any of that, yet, and I'm going to suggest that assuming all of those things infantilizes Day in much the same way that people keep pointing out his family doing, by making him a victim of his family's behavior instead of accepting that a lot of his isolation is self-imposed. No, his family isn't doing things perfectly (redesign your kitchen for function instead of form, when even sighted people are stubbing their toes, for god's sake), but why automatically assume his family did all that to him instead of assuming that Day, himself, did those things, or at least had a hand in them?
What we know at this point is that nobody except Day, himself, shut him up in his bedroom like a hermit and demanded that food be left at his closed door so that he didn't have to interact with anyone, even his family. And once he's made up his mind about that, there's only so much persuasion and so much coaxing and so much fight you can have with a grownass person when they've decided they're not going to do a thing. If Day is going to refuse to come out of his room, he's not five years old, and they can't drag him out - physically cannot, I mean, not without someone getting hurt, plus that's also assault. (The discussion of five-year-old autonomy, when they actually are small enough to pick up, is for another time.) And then try to repair the relationship after you've done something like that. Mork tricks Day out of his room with the fish tank gambit and finds ways to keep tricking him to stay out of it. Nobody has (figuratively) locked Day in his room the way Heart was; Day has walled himself off.
So, I'm wiling to wait to hear if Night and Mom have just decided to tell everyone Day's abroad to hide what's happened to him, or if Day was involved in that cover story, if Day has used that to hide himself away and avoid having to talk to former friends and acquaintances in this new state of perceived vulnerability. And if we never hear for sure, I'm willing to not just assume that this was something imposed on Day against his will, based on what we've seen and learned about Day so far. He has enough internalized shame to do it, himself. When he gets his cornea transplant, he tells Night in Ep 1 - and it sounds like he expects it to happen fairly soon, and he probably expects that a lot of things will go back to normal then, and that this will all be a bad dream, so why not treat this entire time as some sort of liminal space, a time out of time, away from everyone and everything, and never let them see him like this? Why not just go back when he's himself, again?
When he wants to, Day is perfectly capable of pushing back against people who he's absolutely smart enough to know are infantilizing him, from his bratty behavior in the caretaker interviews, to the way he's apparently gotten rid of several caretakers in the past, to the "fuck you" of following Night into the Shining Institute instead of staying in the car. If my dude wanted a cane to help him maneuver, he would have one. Until they prove it to me that he doesn't already have one, tbqh I'm going to suspect that he does, and that he shoved it in the back of a drawer and buried it with other stuff - if he didn't break it over his knee and throw it in the trash. Do you think Mom isn't going to give Day whatever he wants? Day's mother may not be doing everything perfectly, but she is not Heart's mother. And anyway, he's a grownass person with a phone and a computer he's able to use, why are we assuming that Day can't get online and order a cane for his own self, instead of waiting for his family to do it for him? He could get Aon's help, if he needed help with it.