for an out of universe reason, it's because they don't want her to be as weak as aang was at the start of his series, because that would be weird after how much ass he was kicking by the end of it. this is why she starts out knowing firebending, waterbending, and earthbending so well. but at the same time, they need to make it so korra still has a lot to learn, so that she isnt just a deus ex machina that gets no character development. so they have to make the threats into something she doesn't have the ability to deal with, and then they also have to give everyone else a corresponding scaling-up of abilities so they'll still be decent backup
in universe, the fact that it was once believed that some skill is exclusive to the avatar doesn't necessarily mean that it really is. ancient knowledge is sometimes wrong. once upon a time the fire nation thought, based on generations' worth of evidence, that it was a good idea to keep earthbenders trapped in a metal prison. but since then it's been clearly demonstrated that that is not effective. so if there was previously a belief that only the avatar could calm spirits, i don't think it's a problem that we now have a counterexample. i'm not totally sure that was ever said, though. it seems to me that calming an individual enraged spirit is not quite the same thing as the avatar's "being a bridge between the physical and spirit worlds". i havent watched the original show in a while though, so
also i don't understand why you think only the avatar would be able to see it. these spirits look nothing like anything from the first series, so why should they work the same way?