Plus battery life is the first thing to go when they aim for thinness.
I know they've improved battery life in the SE, but still, overall the trend is thinner with a smaller capacity battery (but more efficient components, so you ultimately break even).
I have a phone with a 3100 mAh battery @ 5.1" 1080p, it isn't the thinnest phone around, but boy does it last three or four days. It is super nice. We need more phones like that.