A USB Battery Charging port can deliver 1.5 A of current at 5 V. My iPhone 8 for instance came with a 1 A charger, so I can't assume that it'll use more than that from a USB A socket (it can however use USB Power Delivery with a USB C cable).
Do any iPhones take advantage of the higher current from a USB Battery Charging port?
Wikipedia has this to say about USB Battery Charging:
The charging device identifies a charging port by non-data signaling on the D+ and D− terminals. A dedicated charging port places a resistance not exceeding 200 Ω across the D+ and D− terminals.
Per the base specification, any device attached to a standard downstream port (SDP) must initially be a low-power device, with high-power mode contingent on later USB configuration by the host. Charging ports, however, can immediately supply between 0.5 and 1.5 A of current. The charging port must not apply current limiting below 0.5 A, and must not shut down below 1.5 A or before the voltage drops to 2 V.
Edit
So, if a device draws more than 1.5 A of current from a USB A port then — to me — that suggests that the device is not in spec with regards to USB Battery Charging which, according to the above quote, can deliver a maximum of 1.5 A. My conclusion would be that in that particular instance the device is using some other scheme of determining how much current to draw. That doesn't preclude the existence of support for BC as well, naturally.
I took an interest in USB charging recently while repairing a USB A power bank, and started wondering whether this BC standard is actually being used by devices. Since I have an iPhone I thought it would be a good candidate to ask about.
While I get the impression that my phone does take advantage of higher current, it is purely anecdotal and that also doesn't preclude the possibility that it's using some proprietary method.