There is a reason for the Indo-europeanist tradition, which is a
question of accuracy, or rather lack of it. Consider the glottalic
theory versus the traditional one. Both have problems. One cannot
be sure if PIE *d should be represented either as /d/ or /ť/. The
phonetic symbols convey a level of accuracy that may never be met.
Nor can anyone say if the PIE *e was pronounced as /e/ or /ε/. What
is represented as /bh/ can could be realized as breathy
voiced, aspirated voiced, or aspirated voiceless consonant,
depending on the theory one is more confident with. There is no such
accuracy on the phonological reconstruction so as to represent the
reconstructed forms with phonetic symbols instead of letters. It
would be like represent a measure of 5 cm taken with a ruler as
50.00 mm, as if it was taken with a micrometer.
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Please notice I was referring to Ancient Greek and Proto-Germanic, not the entity called "PIE", which in my opinion is a *fiction*, albeit a convenient one. In such a context we should speak of *phonemic* rather than phonetic values. This is why e.g. the traditional "voiced apirated" /bh, dh, gh/ (/bʰ, dʰ, gʰ/ is a *misrepresentation*) convey just a little more value than pure *algebraic* symbols like those intended for the so-called "laryngeals" (h₁, h₂, etc).