Cordelia is certainly not defensive, she's frail as hell. She's just the archer with the highest attack in the game (even higher than Brave Lyn) so she holds a Brave Bow well. She does indeed get one-shot a lot, but she's a glass cannon. Although for what it's worth I prefer the Death Blow version of her over the more common Life And Death build because it survives a lot more single hits and is still relatively difficult to double (at least on my team that tends to run Spur Speed and Drive Speed). I also run the Escape Route from her base kit because she does tend to get dropped to nearly dead by a lot of single hits, and once it's active it becomes really easy to keep her out of harm's way for the rest of the game.
Brave Lyn outclasses Bride Cordelia in a lot of ways, but Cordelia does still have higher stats in every category but Res and movement. Lyn's speed is higher if she uses Mulagir, but since the whole point of BCordelia is Brave Bow I guess it makes sense to assume Lyn is also holding a Brave Bow. I think Lyn is the best archer in the game, but she doesn't necessarily completely invalidate Cordelia either.
Lack of mobility and high-end buffs over Reinhardt is valid I guess, there's definitely a school of thought that everything should be compared to Reinhardt and there's no reason to ever use anything that isn't Horsey Emblem, and I don't really have a counterargument for that. If that's the way you want to look at it, fair enough, she probably is unplayable. But enough people in tiers 18-19-20 seem to choose not to play Horsey Emblem for one reason or another that she surfaces a lot in arena battles for me. On one hand that seems like it makes a dedicated anti-archer unit more valuable, but on the other hand it's not like taking her out before she can attack is really that difficult. Similarly Brave Lyn has been much less of a problem than I expected because her high speed means she tends to separate herself from the rest of a non-Horsey Emblem team to be easily picked off, and on a cavalry team she's far from the biggest problem anyway.
Edit: I think I'm going to start tracking arena usage again for a while. When I stopped keeping track Reinhardt was in the middle of his upswing and the popular units from the first wave (Takumi, Camilla, MRobin) were on the way out. It'll be interesting to see how things have changed. I expect to see Hector and Reinhardt at the absolute top of the list as well as Azura, Olivia, and all of the best cavalry units, but maybe there'll be surprise all-stars like Tiki was before. Gathering information will be a lot easier now that Arena Assault gives access to endless arena team compositions at no cost too.