TL;DR: (More Corrin talk)
I don't agree with this, I
do think it matters. Some characters might be stronger at lower levels (like King Dedede or Bowser) and some might be weaker (like Joker or Pikachu) compared to top level, generally speaking, but relative strength still matters.
I think it's important to keep in mind that there is a difference between
perceived tier list placement and
actual tier list placement. Sephiroth is a good example of that. Many people, including me, thought Sephiroth was a top tier when he was released (and others thought he was a high tier or a mid tier). This didn't change his
actual strength. I picked him up (thinking he was fun to play, and I still do, and thinking he was incredibly strong, but I don't anymore). I grinded him online for about a year, played two offline tournaments, and dropped him since I noticed significant flaws (mainly dying before getting wing being super stressful in bracket situations).
So, with your examples of Aegis and Sephiroth: Of course they'd play the same, they haven't been nerfed (well, technically Aegis was a little bit). People were mistaken at some point about their placements (either Aegis was overrated at top 5 or underrated at top 15).
If like, Reddit decides tomorrow that Corrin was overrated and carried by strong players and decide to rank her in mid tier, would that change my results? No, of course not. I would believe that Reddit is mistaken and underestimating her and I might be a bit annoyed with that (though granted, I also find it annoying when people overrate my main, which happened often back when I was a Lucina main).
In order for Corrin to actually be mid tier and not just perceived as such, I believe at least one of the following has to be true:
#1. I, and many other, severely overrate her for various reasons and she has greater flaws than we expected.
#2. The meta changes to make her bad MUs more common for some reason (like Sheik, Snake, and Sephiroth).
#3. We get a new patch that nerfs her.
#2 is an interesting point, by the way. How good a character is also depends on the environment it's played it. If your locals have a lot of Snakes and a lot of Sephiroths, Corrin is likely going to do worse than in locals filled with Marios and Min Mins. Even a Snake main might suffer in a local filled with Ness mains and G&W players. My locals happen to have a relatively hospitable environment for Corrin (the only MU I even consider slightly losing is Samus and maybe Ridley, otherwise it's all even or winning MUs for Corrin at my locals). So even if she were, hypothetically, a mid tier she might be a mid tier who would do well at my locals.
Anyways, I think it's largely hypothetical anyways. Corrin being a mid tier seems about as likely as Palutena, Wolf, or Roy being mid tiers (ie not very likely at all).
Oh, by the way: Back in 2020 Corrin got buffed. I thought the buffs were massive and thought it made her a high tier and really strong. While I had played around with her from time to time before then I thought she felt a bit too weak and needed some number adjustments to really shine, and well... Patch 8.0.0 sure gave her some number adjustments. Cosmos started playing her again and I picked her up too. I thought she was top 20 (Cosmos thought she was top 15) and about as good as in Smash 4. I had a lot of fun with her. Then December came and Sephiroth dropped. I thought he was top tier and really fun and stronger than Corrin, so I picked him up. As I mentioned, I played him for about a year and then dropped him and picked up Aegis. At the time I no longer thought Corrin was top 20 (Cosmos had dropped her and SHADIC was just 14-15 years old and Neo hadn't popped off yet).
I picked her up again in June 2023 (I thought she was around top 30 at the time). I'm looking back at some of my old Discord messages and seems I was toying with the idea in 2022 but ultimately didn't do it for three main reasons: One was that I thought Aegis was so much better, another was that I didn't really want to invest the time into making the swap (although admittedly Corrin would be easier to pick up than many others since I played her in the second half of 2020 and in Smash 4), and the third reason was that I enjoy having top players playing a character, and at the time it was mostly SHADIC doing well with her. In 2023 Neo changed that... Neo's early 2023 was really strong, and he ended up #33 in the mid-year rank, and #30 for the whole year. Having both Neo and SHADIC to watch (and SHADIC has been doing really well lately, he's starting to look like a top 30 player or maybe even top 20) is a privilege. Sparg0 and Aaron are nice too, although I'm not convinced either of them will stick with the character (but if they do that'd be super cool).
I thought Corrin was high tier back in 2022 but probably more like top 35-40. And now I think there's a case for top tier, (although I'm not sure, she could still be high tier, she's probably somewhere between #13 and #30, hah, so many variables).
Speaking of not being sure about tier placements, I made a list of which characters I think could be in which tier. This is
not a tier list, and it is ordered alphabetically. Basically, I'm only sure about a few characters being in top/high/low tier. I'm not actually sure about a single character being in mid tier (some of they might be mid or secretly high tier, some might be low or mid tier). This should also not be considered ordered either, just because a character is in "Not sure if top tier or high tier" doesn't mean it's necessarily stronger than "I'm sure thery are high tier". Like, on my actual tier list I'd put Mii Brawler lower than Lucina, Sheik, and Zero Suit Samus, but I think there's a slight chance that ESAM and some other Mii Brawler optimists are right and that Brawler is a secret top tier (atm I don't think he is, though).
I don't think Banjo or Link are high tiers, but I could see them potentially being high tier when pushed to their limit. I could also see them potentially being low tier.
Based on this, I seem to think 29 characters have the potential to be top tier. I don't actually think all of them are top tier, though. And seems 61 characters could be high tier or higher, but yeah, I don't actually think that's the case.
Is Corrin top tier? I think she might be. It's also entirely plausible that she's high-high tier. Sparg0, when asked, said he doesn't think she's a top tier, he thinks high-high tier. Fair enough. Last I heard Neo also doesn't think she's top tier (he thinks Corrin players are really good though and are making her kind of seem like a top tier because of that). I don't know what SHADIC thinks but he's believed in Corrin for a long time (he thought she was a high tier before 8.0.0, and in retrospect it's possible he was right, she was certainly at least somewhat underrated at the time). Aaron thinks she's top 10 or top 5 (very optimistic, probably a bit too optimistic but maybe he's seeing something the rest of us aren't).
I'm still at the point where I'm pretty content with Corrin being placed in top 30. I'd like her to be placed higher, but I realize it's going to take some time to get over years of people viewing her as a mid tier.
I actually think Corrin might be better in this game compared to 4. She struggled more vs meta characters in 4 + many of the changes from 4 to Ultimate buffed her (patches included). That being said, she's deeper now compared to 4 and takes more effort to learn. She also doesn't gatekeep characters as much (I don't think she has any +3 MUs in this game while she had some in 4, pin kick away is not safe anymore and pin cancel/pin jump are strong but there is counter-play, so she can't destroy characters like Kirby or Ness quite as easily as in 4 anymore). Still, I believe she has a very favorable MU spread overall, and has the potential to be a top tier or at the very least a high tier.
TL;DR: (More Corrin talk)