Agreed, and I do the same. I don't like it being on all the time so it's unplugged while not in use.
As for soundstage, try adjusting the EQ on you're device itself, not the amp. I use mine for Spotify, when I adjust the EQ I get the sound I'm looking for. The lower end did sound a little muffled, but some adjustments to Spotify cleared it right up. I've spent hours using the 3.5mm jack and swapping back to the BT adaptor... I can't tell any diff. The Sound quality from my phone is already compressed so it's not like we are starting off with hi-Rez flac files. So for what it is, it works fine for me. I've not tried other apps, and I do use the Spotify extream setting. I like it, I may invest in the Douk Audio one, I've seen some good reviews on it. Looks of great quality... I'll post some pix if I do pick one up.
Kind Regards,
John