It is interesting that you say this -- I have not tested the microStreamer with and without additional battery power, but I suspect that the limits of the iPhone power supply could affect the output stages of a DAC/amp in terms of its amplification performance. It is clearly the case that the CCK/Lightning-to-USB does not provide full current to the USB spec; otherwise there wouldn't be the "too much power" message in the first place. I also doubt that the microStreamer's headphone out was designed with power limits in mind (the iPHone capability was only made available after a firmware update).
What I usually do with the microStreamer now when using it with the iPhone is pair it with an amp, in this case a FiiO E12DIY. This makes a mini-stack that is still pretty compact. The microStreamer is ideal in this case as it has a dedicated line out -- not all portable DAC/amps do. I think this gets over any remaining issues with power to the microStreamer as only the DAC on the microStreamer is in play.