I have 2 echo dot's and BOTH have this same problem. After disconnecting from BT it sounds like an old AM Radio, I have to reboot them to get back to normal.
Not sure when it started, but not long ago for sure.
I tried to talk via CHAT with some guy in Amazon (India I think), and was not able to even understand the problem.... hope someone has better luck than me to report this, cause this guy gave me a 15% discount... not sure WHAT he understood but for sure, not the problem.
Of course, I can't replace both with that discount and I'm not even the US so.... hope they fix this.