This assumes you’re powering the phone solely off the cap. Even with a battery you’d still need something in the mF range to make up for the battery’s degradation.
> [only able to use the cap from 4V to 3V]
> (C * 1V * 1V)/2
> [you'll need 1000mF]
Wrong equation. That's the energy from 0V to 1V. Each incremental volt stores more power than the last. 0V-3V is 9x that amount, and 0V-4V is 16x that amount, so 3V-4V is 7x that amount, and you'll need 140mF.
But also it shouldn't be connected directly in parallel to the battery; so I'd think of it more as 4.2V to 2V of supply. That would mean you need 74mF.
So put in two and you'll more than hit the target.
Even better, if you expect the battery to contribute some, you only need the one.
When you open your mail and it has to perform a sync, for example, the transient may last for 10+ seconds and it’s not something you can fix with a supercap. You’d be better off adding more battery at that stage, as a larger battery has lower proportional sag for a given current (coulomb rates).
Another thing you can do is size your battery, say 20% larger than you require it, and only charge to 80%. This reduces ageing significantly, BUT consumers would never see this as a feature. They would just complain that the latest Apple phone has 20% less battery than the competitor and is $50 more expensive and heavier than the last model.
I’m taking it at a punt that 99% of regular consumers want to change their phone every 2-3 years (to get the latest camera, Face ID or car keys or whatever feature it might be), so that’s what Apple has targeted for the maximum age of their battery. Anything more is making a collective trade-off for the, perhaps, 1% no?
Those phones just had tired depleted batteries and the proper thing to do was offer users battery replacement, not lie to their faces while upselling new model.