TBH, yes, it is really that expensive to rent if you're not looking at ex-council - and having come to know this city like I have, I don't blame you there - or farther out. You're also looking for a three bed w/a garden.
Much of Edinburgh's housing stock is flats w/two bedrooms(although many of the Victorian ones have a boxroom big enough to be a third bedroom) and a communal garden at best. The newer flats tend to have car parks instead of communal gardens.
Houses are not as plentiful so to rent them can be costly.
We pay £500/month for this two-bed flat on the 2nd floor. And that's b/c it was unfurnished. We looked and looked. That was pretty much the going rate. Many were furnished and they wanted even more money.
The council tax - water, sewage and rubbish collection are rolled into your bill here if you live in a flat, no meters - will be £150/month come April, up from £131. And this is only Band C (the scale goes to G).
It's just not a really cheap place for families to live, so many families have moved outside the city limits.