The A1 is a simple product with a clearly defined but limited purpose: It takes the too low (but ideally clean) audio output from a mobile device and adds a bit of oomph and control to it.
In the case of my current phone, a Sony Z3 Compact, this is much needed for most headphones. I’m talking real life IEMs and on-ears here, not even exotic hard to drive ones. While this is an especially bad example, headphone outputs overall have gotten worse in regard to what they can put out in recent years generally.
With the A1, something not wildly efficient like the Sound magic E10 becomes usable. Somewhat to my surprise they’re even enjoyable. I can turn them up to a level where the resolution becomes decent, and they benefit from better control over the bass.
Apart from the oomph, the output also stays clean better under load. The Z3 can drive my Shure SE535, which are exceptionally sensitive, to more than decent volumes, but with the A1 a bit of coarseness in the treble is gone, and the bass control and extension improves. I generally find it more enjoyable to listen to music and get lost in a track much easier when I use the A1.
So: If your mobile headphone output is somewhat lacking in volume with your headphones, the A1 is well worth a try. If you’re content with the volume, but wonder what you can do to improve the playback quality on some good, but not really hard to drive heaphones then the A1 makes so much more sense than getting into other areas such as the ridiculousness of cable upgrades.
Disclaimer: I bought any products mentioned here myself.