People are already carrying phones that thick with an Otterbox. I would happily take that phone, provided it solves my pet peeves. (and they make it look a *little* nicer)
A STELLAR radio/antennae
I'm near the end of life for my Verizon GNexus. Let me make it clear. I *LIKE* this phone. It's the best I've ever had, but these are the issues that drive me nuts. I've had it with shit radios. I get BLAZING 4G speeds outside. I take a step in a building, right next to the window and it CAN'T WAIT to jump to 1 bar of 3g if I'm lucky. My wife's *&%#ing iPhone has a great signal. It's humiliating.
Battery life
Yes, a few days would be great! I'd like to leave my features on. I use 4G and Bluetooth all day long. Thankfully, I can sit next to a charger all day. Good thing. God forbid I go out for the evening and forget to turn off all the useful things a smartphone does. There's a reason I have 4 spare batteries.
A *LOUD* %$*)ing speaker!
For god's sake. My Droid 1 had an excellent speaker. It's like Samsung's speakers are afraid to speak up. If you pump them up with an app, they sound like crap. Give me something that's ANNOYINGLY loud so it's actually useful for it's purpose. There shouldn't be such a big market for Bluetooth speakers.
Storage
This wouldn't be such an issue if the carriers hasn't ripped away all the unlimited plans. Either provide a SD slot or make it 32gb minimum. 8GB premium phones? In 2013? WTH?
Skins and bloat. (Unrelated, now I'm just ranting)
Make this crap available as launchers and apps available in the app store. Let Google, and Google ONLY, worry about the OS updates. Don't hold my phone hostage because your don't want to lose money updating your feces software on a one year old phone that's already "End of Life". Give us the easy option of easily and completely uninstalling. If your skin or bloatware really that compelling, we'll WANT to keep it. Heck, charge $.99 , and if it's really that great, make a profit.
Edit:
Make it waterproof/dustproof/and ruggedized... Those are already options on other phones. Just make an "un-iPhone" Function over form...