Why do Spartan Neohomoioi Thorakitai not have any chainmail armour?

[Aodh Mór Ó Néill]

Its the "Spartan interpretation of Thorax troops of other Hellenic factions", but unlike those troops, they're noticeably lacking in the chainmail department. Is there a specific reason for this?

[KAM 2150]

They are not thorakitai per se.

Thorakitai in their name refers more to their reform tier than anything else.

Its just 3rd stage level of Spartan hoplite upgrade tree, where first guys represent poor period of Sparta, which you can see in their armors, second unit is the standard Spartan hoplite of late period and third unit is just showing them as very rich Spartans since you need to grow rather large to reach them, hence why they look on average as officers in most other units.

Sparta never got to developing on thorakitai units and they also never adopted thureos shields (but probably their allied states did), instead switching to pike phalanx near the end of 3rd century BC.