Midwives really dislike them as you don't know what you're listening for. The midwife that did my doppler took a good 5 mins to find baby, and even double checked by holding my pulse in my wrist while listening to what she found to make sure was different and wasn't just mine again. Several sounds in there - your pulse, digestive system etc.
You're not trained to find the right thing so people end up panicking because they can't find anything they think is right, or for example feel reduced movements, check with the doppler, find their own heartbeat and think it's the baby and is fine so they don't go in to get checked out and actually there was something wrong. It can give false reassurance as well as false concern.