Again, this depends on the traditions of the Local Church. As has been mentioned, Churches in the greater Slavic tradition tend to allow, and in some instances even require, Readers and SubDeacons to wear the inner cassock at services and on Church business - even when they are not serving.
In the Byzantine tradition however, only the "on-duty" Reader wears a cassock, and it is the outer cassock (the one with the wide sleeves) without
the inner cassock, just over his street clothes.
It would appear that in Romanian, and Ukranian Churches (at least the UOCC parishes that I've visited), the Reader does his job in his normal clothes.
That being said, I've also seen many Readers in Russian, and Russian descendant, Churches that weren't wearing cassocks either, simply because they didn't have one. I'm pretty sure a few are not interested in getting one if they don't absolutely have to, because they're expensive!
So, it comes down to varying traditions within Orthodoxy, and/or the ability of the Reader or SubDeacon to purchase an cassock.
I'm sorry, Noesisaa, but the Romanian Church is not the measure by which all the other Churches are measured.