I don't know why Mother Courage tells people not to stay on the Asian side, but we absolutely loved the Kadikoy area and lived there for six months.
THAT is exactly why, Chris. Living in a place for six months isn't the same as a short stay - especially if it's your first time. In fact, after visiting Istanbul for many years (first time was 1969)and much as I love walking in and exploring the Asian side, I still find Sultanahmet a useful area to stay. (and that's without 'pushing' any particular hostel, as I gather you've been doing.)
For first-timers there's simply no contest between being able to walk to a site in 10 -20 minutes and taking a 15 minute ferry plus 10 minute tram ride just to get amongst those iconic and ancient sites.