Australian saddles are designed for a bit of a chair seat. No, it won't hurt the horse's back.
It isn't good or bad. It just depends on what you are doing and why. I find my mare tends to calm down a bit when I adopt a bit of a chair seat (pic below). It is good if you anticipate quick stops, or unexpected stops.
For a tight turn, heels under hip works better.
Jump saddles normally put the stirrup bars a bit farther forward than a dressage saddle. Below is a picture of Gen Patton in a 'military seat' for jumping:
The picture below was taken from a George Morris book where he used it as an example of good riding:
Notice if you drew a vertical line at the stirrup, almost half of her weight would be in front, so she is balanced just slightly behind the stirrup.
Here is how I figure it - and I'm not a trainer or instructor or an anything, so take it FWIW - I think the stirrup strap should be vertical and your rump at the lowest part of the saddle. If you do that, you are riding the saddle the way it was designed to be ridden. If you anticipate any unplanned stopping or just want to stretch your legs, stick your feet out a little. It will help you get your heels down, too. If you want to spin or make a tight turn, bring your heels under your hips so the horse is free to pivot under you. If you want to excel in a particular sport - jumping, dressage, reining, etc - do what your teacher says, or what the folks who are champions do.
Oh - and western saddles are really designed, in most cases, for a chair seat: