Is distant counter worth giving to Ayra?

In my opinion, the only reason for Ayra to ever have DC is for arena scoring... I think her res is too low for her to effectively use DC. Maybe if you have her to counter specifically Halloween Jakob? Which is the only ranged physical unit commonly seen in high tiers... Other than that, I really don't understand why they suggest her running it...

That's because GP's optimal builds are full of bias with 'DC is the best skill'. Even though, in my opinion, a good hit from a strong mage or distant unit like ANY blue mage or strong bows/daggers like Sothe or Brave Lyn will outright one-shot her, rending DC worthless.
Listen, build her how you want. DC doesn't have to be on her, it's just an over used skill that's blow out of proportion with it's usefulness.
(It's a good skill, I am not denying that. But it doesn't NEED to be on her like GP presses you to do)

She ends up playing like Ryoma, but with a more spammy and busted special. The idea is so that she's able to use Regnal Astra every single turn once Wrath's conditions are met. They might call it an "enemy phase" build, but there's no skill that makes her more advantageous during the enemy phase. If anything, it's a player phase build so she can attack with her special without having to suffer any hits so long as the enemy doesn't survive her Regnal Astra. Why offer the enemy a free attack when your Regnal Astra is fully charged each turn?

Depends on how much you benefit out of her trying to replicate Hector minus the disgusting durability...her physical bulk can be really good, assuming she is +Def. But then she misses out on reliably tanking most mages, and even Blade Tome Nino likely does a number on her (potentially doubling, considering even +Spd Ayra with Distant Def is likely to get doubled by her).

Truth in the matter is, she's far better off just shredding everything to pieces in her own phase than trying to force a generalist role. At best, I'd see it as a bothersome fly when you don't have a Reinhardt or strong Blue in your Defense team.

Do it If she's you're summoner support and you're switching to Slaying Edge and Wrath. Otherwise just keep her base kit

I slapped my only DC on my Ayra (+SPD/-HP) who I summoner supported and I regret nothing. Her special nukes almost everything she touches. Just give her the distant defense seal.

Take my opinion with a grain of salt since I don’t have Ayra, but my impression is that while Ayra can get some use out of DC, it’s not her best choice for an A skill. My impression of DC these days is that it’s like Galeforce was in Awakening or Replicate was in Fates: it seems like such an OP skill that everyone wants it on as many units as possible, without regard for who can actually make good use of it. Especially in this game where DC fodder is extremely limited, I’d save it for someone with a higher res stat than Ayra.