I would say yes to suspecting Costa, it is so good against defensive teams that they literally just faint upon it's stare. It has an answer to the multitude of physically defensive Grass types in the form of Ice Beam, which also checks Roselia, the most threatening Pokemon in the tier behind Carracosta itself. This is something Barbaracle lacks, not to mention it is strictly a physical attacker, and walled more easily. It is also crippled effectively by its walls such as Roselia and Gourgeist-S. I think Carracosta should get a suspect but Barbaracle should not.
However, Barbaracle still can deal enough damage to most of its checks with Aerial Ace or X-Scissor...
+2 252+ Atk Tough Claws Barbaracle Aerial Ace vs. 252 HP / 252+ Def Eviolite Tangela: 146-172 (43.7 - 51.4%) -- 98.4% chance to 2HKO after Stealth Rock
Which should be the bulkiest thing that could be stopping Barbaracle...
And some others like Defensive Gourgeist Super:
Aerial Ace vs. 252 HP / 252+ Def Gourgeist-Super: 190-224 (50.8 - 59.8%) -- 84% chance to 2HKO after Leftovers recovery
Also, something like Roselia shouldn't exactly be considered a counter since:
+2 252+ Atk Tough Claws Barbaracle Aerial Ace vs. 252 HP / 252+ Def Eviolite Roselia: 250-296 (82.2 - 97.3%) -- 68.8% chance to OHKO after Stealth Rock
Which means that Barbaracle has a decent chance to kick out Roselia at +2, just with one turn of setup and considering the use of White Herb... And u know what? It can even be evd to handle some super effective attacks like Scarf Raichu Thunderbolt...
252 SpA Raichu Thunderbolt vs. 0 HP / 68 SpD Barbaracle: 240-284 (84.2 - 99.6%) -- guaranteed 2HKO
Those Evs can be taken from speed, since even without those is faster than Jolly Carracosta (with just 192 speed evs, reaches 220 speed, one pont faster than fully invested base 60 and 440 speed at +2, being then faster than the whole unboosted tier...)
That kind of things let Barbaracle be as tough as Costa even without being mixed... Don't think that I'm dismissing Costa, since that thing even being slow as heck, its also powerful, bulky and has STAB priority but I personally think that Barbaracle is just as broken as Costa!