Seekers are an upgraded Templar in terms of ability. Read Asunder. Lord Seeker Lambert has the same abilities any Templar does.
Why would it not make sense if Cassandra, a member of the Seekers of truth, an elite subsection of Templars, has Templar training?
Not all Seekers are from the Templars. Cassandra is one of these exceptions since we see the story of her becoming what she is.
Well, it'd make more sense than Blackwall with Templar rather than Champion...
How would it make more sense for Blackwall to be a Champion rather than a Templar? We don't know his past yet other than he has been a Warden for a long time.
Plus Carver received Templar training while in the Wardens.