That probably has something to do with Thrask being a liar who allies with Blood Mages and has someone dear to the Champion kidnapped and almost killed because he was too stupid to see how far gone Grace was. Nice guy, I'd probably have him over for dinner, but he was hardly the model Templar.
Evangeline is only slightly better. She's a betrayer. She has innocent blood on her hands because she is at least partly responsible for the Mage Rebellion, and she's a coward. Rather than stay and attempt to fix things, she runs and hides, doing exactly nothing useful until the Inquisition comes for her and Rhys.
Was just going to say this. They gave up. Evangeline and Thrask (and Cullen, let's make this fair) are all good people, but they're not "ideal Templars," because they gave up on the Order. Instead of staying and trying to fix what was wrong with the Templars, they threw their hands up and peaced out. I love these characters, they're good people with good hearts and deserve respect for holding on to their own convictions... but they're not ideal Templars, if their response to crisis is giving up.
Barris stayed. He stuck with the Order to the end, trying to uphold the ideals of what the Templars should really be about even against impossible odds, even with his superiors, the rebel Templars, and pretty much the whole world against him. He lives and dies by the ideals of the Order, and only gives up if you force him to, if you disband the Order he's been fighting to save, so he has nothing left to fight for. That's an "ideal Templar" to me - one who will stay with the Order through thick and thin, who will bring it back to reason, reform it, weed out the corruption and shape it back into what it should be.
There's room to love all four characters for who they are, but Barris definitely takes the "ideal Templar" badge over the others.