I’m not convinced standardised batteries are required. The vast majority of people are using only a small number of phones. A battery store could easily stock the batteries for every iPhone model. The real problem is how hard it is for the average person to replace them.
It would be quite a bit thicker than most phones today, but not outrageously so--about as thick as my last pre-iPhone phone (a Palm Treo). We had no trouble carrying such thick phones around back then, and those were the days when we were also carrying our iPods or portable CD players around too.
Here are the battery capacities of various iPhones.
iPhone SE: 6.7 W h
iPhone X: 10.3 W h
iPhone 11: 11.5 W h
iPhone 11 Pro Max: 14.7 W h
Low self-discharge rechargeable AA MiMH batteries are available with capacities of 2.7 W h.
You'd need 3 of them to match an iPhone SE, 4 for an iPhone X, 5 for an 11, and 6 for an 11 Pro Max.
An AA battery is between 14 mm and 15 mm in diameter. That should be an upper limit on how much thicker you would need to make the phone.
Would there be enough people who would like the convenience of using off the shelve rechargeable NiMH AA batteries for such a phone to sell despite 14 mm more thickness?
I have no idea.
https://www.amazon.com/KENTLI-Rechargeable-Battery-Lithium-i...