(Pianist here) But there is no objectively correct fingering, it's just what feels best/easiest/smoothest for you, personally. Having to read the fingering as well as the notes just seems to make it more complicated.
Even for the simplest music, say a C major triad chord in the right hand - C-E-G - you could play it 1-3-5, 1-2-4, 1-2-3, 2-3-5 etc. I have big hands, so 1-3-5 feels the least comfortable of those, although it may be the 'automatic' choice. I agree with what others have said, that learning scales and arpeggios teaches you almost all you need to know about sensible fingerings on piano, and then having fingering pre-written on any music is entirely unnecessary. Books of scales and arpeggios have fingering written in, which you should learn.
