It does have sunflower seeds and whole peanuts
Our last Syrian had it all his life and loved it - never left a thing. And he lived to 2 years 8 months. I think it's an easy option for beginners as well without having to worry about percentages etc. Variety can be added with extras but it has the basics needed.
Anyway! Looking back through Creampuff's other threads it seems the hamster is a Syrian so there are other options! Although I'd still say Harry Hamster is a good basic diet for a beginner. Don't get Oxbow Essentials though - despite the reviews it is not a good hamster food (is that the pelleted mix you're using). Higgins Sunburst looks ok but is a bit low in protein so it would need supplementing. I'm not keen on all the added dried fruits which will have nasty preservatives!
I know it's harder to find good all in one mixes in the US.