It's somewhat subjective, but my problem is how does one name a dyad, apart from calling it an interval. Thus power chord becomes D5 - an interval.
Most chords, to me, need the blend of minimum three notes. Majors and minors will have that interval between root and three. Some will argue, corectly to an extent, that actually the root will usually sound a 5th as its second harmonic, thus it's going to sound anyway - a good reason why some jazz chords leave out the P5. However - if that's the case, is that actually a two note 'chord', as we hear and perceive three notes...
So, what do we call other two note 'chords'? All the 'proper' chord names won't work, as they're specific to the notes in that chord. Taking a note out of even a three note chord stops it being an xyz.
The power chord works sonically because the 3 is missing. Favoured by guitarists using distortion/overdrive. With those effects, the harmonics of each note are accentuated, and those belonging to the 3 clash with the others. Root and 5 harmonics generally sound o.k. together, so it works. But, to me at least, it still isn't a chord, but an interval - a dyad.