Well the time wraiths are very similar to the Black Flash's role in the comics. In there, he is unknown and there are theories just like that about him. Though mine is that he had no prior existence and same with the Time Wraiths. As you got to send them to places before humans ever existed and where they cannot breathe.
Barry was in the Speed Force and many others that were not time wraiths.
People can be in the Speed Force without becoming time wraiths. That doesn't prove anything.
People can breathe in the Speed Force and on places were the Time Wraiths and the Black Flashgoes as well.
I'm not talking about the Speed Force. That place is breathable. I meant when they need to go before the big bang or any other Time Wraith assignment.
Spirits, demons, whatever you want to call them. Non-corporeal entities generated by the Spped Force or I guess maybe made of Speed Force since similar to how Gypsy can cut off a speedsters powers, sonic frequencies can destroy Time Wraiths. I'd say they can't really be former speedsters since then they'd be more like Zoom.