Re: Slim batteries v. big batteries.
The solution turns out to be some sort of external power bank. Then the trade-off of bulk, weight and duration is in your hands. Phone manufacturers don't have to produce low-volume, fat battery phones. You choose what size of power bank you want to carry around. Or maybe two power banks, so you can be sure to have a charged one whilst the other is charging. Lighter phone means less arm strain from long phone calls. I expect you can think of other advantages to this solution.
Tesco even do an environmentally unfriendly one-shot power bank, discussed and dissected by Big Clive. Rechargeable Li ion cell, missing the circuitry that would allow it to be recharged.