Ancient Greek: why is there no neuter first declension nouns?

The original Indo-European declensions were thematic (corresponding to the Greek second declension) and athematic (corresponding to the Greek third declension).

The first declension was a late innovation in Proto-Indo-European, involving a suffixed –e[math]h_2[/math] > -ā. It postdates the split of Hittite.

The masculine first declension nouns were an even later innovation, and they were specific to two patterns: the agent suffix –tās/tēs, and adjectival compounds like chrysokomēs ‘golden-haired’. Sihler just shrugs his shoulders about –tās:

The functional specialization of the type as an agent noun is partly the result of its coincidental similarity to inherited -τηρ, -τωρ [the more archaic agent suffix]. Why the formation would show an early and striking partiality for masc. ā-stem inflection, rather than (say) masc *-τος, fem. *-τᾱ, is however an enigma. (§267)

The adjective ending on the other hand looks to me a pummelling of a feminine noun into a masculine: χρυσὴ κώμη ‘golden.fem hair.fem’ > χρυσο-κώμη-ς {golden-hair.fem}.masc.

So, the first declension originated as a feminine declension. A masculine first declension was tacked on in proto-Greek. There was never any driver to add on a neuter first declension as well: there was no agent suffix or adjective formation that would make it happen. But that’s just randomness as much as anything.