Okay but in 12-TET, there are only 12 notes. D# and E♭ are the same note, because there is only one note between D and E. On paper and in practice, the note between D and E is the same whether you write it as D# or as E♭. A piano doesn't know how the note is written in the sheet music.
EDIT:to be clear, I'm not disagreeing with most of what you're saying. 12-TET can't represent the desirable perfect fractions, and in a system which can (such as a just intonation system), the starting point does matter. And maybe a vocalist or a violinist would play D# and E♭ subtly differently, I don't know. My main point is just that in a whole lot of contexts, such as when playing a piano, there is no difference between the notes. Your comment made it look like there's always a difference between theory and practice which makes D# and E♭ different in practice, when that's often not the case. We do use 12-TET in practice.
EDIT:to be clear, I'm not disagreeing with most of what you're saying. 12-TET can't represent the desirable perfect fractions, and in a system which can (such as a just intonation system), the starting point does matter. And maybe a vocalist or a violinist would play D# and E♭ subtly differently, I don't know. My main point is just that in a whole lot of contexts, such as when playing a piano, there is no difference between the notes. Your comment made it look like there's always a difference between theory and practice which makes D# and E♭ different in practice, when that's often not the case. We do use 12-TET in practice.