What is the advantage of non-inverting op amp high pass filter
There is a reason non-inverting 1st order high-pass filters are sometimes used and this is to preserve the dc level in the circuit. It's horses for courses - some designs will want to preserve the DC level, some won't care and some won't want to. It's not a black and white sort of thing.

When it comes to a 2nd order high-pass filter the non-inverting configuration (Sallen Key type) will usually be preferred and this doesn't preserve the dc level: - 



Again horses for courses.