"I don't know the new phone's manufacture date, but I guess it would have to be in the Fall of 2016 at least because it shipped with iOs 10.1.1? So what is different? Is apple shipping iPhones with better batteries? One's that are not adversely affected by whatever "bugs" are in 10x.x software? People who bought the 7/7plus and have battery issues would argue no. " Apple has returned to manufacturers millions of iPhones. E.G. QC issues with the 5, 8 million returns. If you just take the scale of the 6S, over 250 million produced last year, and take for granted that one manufacturer Z (out of, say, 10) made a few million batteries for the 5, 5S, 6, 6S and 7 but not Plus, you can see how the forensics become complex; batch, ser#, manufacturer etc. All mobile device companies are pursuing special power management features; additional controller or power chips; in the next 12-14 months you are very likely to recall what I just wrote. For sure once a bug is discovered, e.g. 6S faulty batteries, a battery manufacturer seeks to correct it. Cannot really argue that Li Ion batteries are getting any better, even if both Samsung and Apple buy good quality parts. It may very well be that 1-3% unlucky draw. 4 million smartphone batteries, minimum, are made every day.
As for software, if you program the code to activate the circuit breaker at, say, -600mAh/hr (or a rapid drain of 3 hours on a 1,800mAh battery), then any phone at that discharge level would shut off. Ideally one wants to target faulty batteries for safety reasons, prevent battery overheating, which is one minor step away from a dreaded fire. Samsung had 55 incidents, 17billion losss... But, if you have Pokemon Go, GPS, and a bunch of other fancy features increasing demand, on a normal phone, I can see how the software would cut of power. Yes, it can be controlled by software. Either case, a good battery can handle a high demand without overheating.
Battery replacement, the industry is moving to sealing all devices. Some people (ask Mjolscure) get kits and in 10 minutes swapped their battery with a 3d part manufacturer. In your iPhone 6 case in your son's hands, that would make you loose the possible replacement with Apple.
Massachusets is summer versus my friends -20 to -30 F in Canada. You are fine. A few snowmobille sessions and any mobile can be bricked.