I know it's been a while since this question has been asked originally but I'm still seeing this question come up, and it's been my searching for an answer to a question like this which brought me here.
USB Y-cables violate the USB specifications and so only work to provide more power to devices that also violated the USB specifications. It should only be a surprise to those that know little about how USB works when or if these USB Y-cables fail to provide more power to an attached device than when connected to a host without the Y-cable. There are ways to make a kind of USB Y-cable to provide more power to a device when attached to a USB host that does not provide sufficient power, and do so without violating the USB specifications. Answering that though is out of scope for this question since that applies to phones and tablets that do not have Lightning ports.
I'll see many complaints on how Apple does things that are "non-standard" but from reading the USB specifications Apple actually complies with the USB specifications very well. Their idea on how their USB-A power bricks handshakes with their iDevices might not be the same way other manufacturers do their handshaking but it does not appear to violate the USB specifications. The original post mentions getting 900 mA from a USB 3.x port and 500 mA from a USB 2.0 port but these are not maximums, these are minimums. A host computer must supply at least 900 mA from a USB 3.x port and 500 mA from a USB 2.0 port to be considered in compliance with the USB specifications. USB ports on Apple computers will supply more than this, and it appears various computers from other manufacturers will as well.
USB 2.0 and USB 3.x allow for devices to negotiate for up to 1.5 amps before having to resort to USB-PD or USB-BC to negotiate for more. As best I can tell Apple computers and iDevices use USB-PD to negotiate for up to 12 watts, or 2.4 amps, of power to the iDevice. Without support for USB-PD, or whatever it is that Apple is using, the rate of charge will be limited to 2.5 watts (500 mA), 4.5 watts (900 mA), or 7.5 watts (1.5 A). The USB spec allows up to 2.4 amps to peripherals connected to hosts by USB-A and Apple computers will happily supply this. Or at least those built after the USB-BC and USB 2.0 specs were published.
If you need power to your iDevice while connected to some peripheral device then the use of a number of Lightning dongles will allow this. Apple builds a variety of such dongles, as do manufacturers that Apple partnered with. These dongles will have a Lightning port for up to 12 watts of power and a port for the peripheral. Examples for such ports include HDMI, USB 3.x, Ethernet, and 1/8" audio for headphones and headsets.
Connecting an Apple iDevice with a Lightning port to a computer that does not provide 12 watts does present a problem if the users wants both data transfer and 12 watts to the iDevice. As far as I can tell there is no Lightning dongle that will split out the power and data so that someone can plug in a 12 watt power brick to power an iDevice while it is also still able to maintain a USB connection to a computer.
Sometimes the problem isn't that the computer is incapable of providing the power Apple iDevices and their users want, it's that the computer and iDevice are not speaking the same language on negotiating the power transfer.
From what I have seen from my research so far a USB dock or hub is not likely to enable a computer to provide more power to an Apple iDevice. The dock or hub might be getting power from somewhere other than the host computer but it is still the host computer that is managing the power transfer. The computer must still speak the same language as the iDevice to negotiate more than 7.5 watts of power. A USB hub or dock might be able to provide 2.4 amps to connected devices but an iDevice will not draw more power than it has been granted permission to draw.
What might allow a connection to a host computer and provide 12 watts to an iDevice is a Thunderbolt dock. A USB-C to Lightning cable plugged into a USB-C port on a Thunderbolt dock may allow data transfer to a Thunderbolt host while providing 12 watts of power. Thunderbolt docks have an independent USB-PD controller, like that in a USB-PD power brick, that does not rely on the host to manage power delivery. The USB-C Thunderbolt ports on such docks will still support the USB 2.0 protocol that will be required to create the connection between the host and the iDevice.
I will emphasize that use of a Thunderbolt dock for getting 12 watts of power while maintaining a data connection to an Apple iPhone or iPad is speculation. It's an educated guess but still a guess. I haven't tested this theory and I don't (yet) have the hardware to test this theory. I wrote this lengthy answer mostly to clarify what I'm seeing as misinterpretations of the USB specs. While this is an older question it is still relevant today and variations on this still come up.