I have constructed two buildings with green roofs, both pitched. One I live in has been in place for 11 years without fault. The other is a large shed which has been up for a couple of years, again without any issues.
I have done these myself due to the fact that contractors charge a ridiculous amount to do the work.
I would advise that you have a modest pitch and use a lightweight growing medium such as leca and peat free compost. Sedum plugs will happily grow in this.
I used the system sold by safeguard chemicals.
See
http://www.safeguardwaterproofing.co.uk/applications/green_roofs.phpIt is easy to use for a competent diyer.
The attractions of a green roof are:
1. Visually less impact especially in a rural situation.
2. Water Retention reduces water run off.
3. Increases biodiversity.
4. Increases thermal mass and reduces summer overheating.
I dont believe they are suitable for all situations and I do not understand why some people are so negative about them.
I also dont buy the embodied energy arguement unless you choose to ignore the fuel involved in mining and transporting slate (??from china) and the environmental impact of mining.