I recycle everything so personally don't have much need for the tether, but it's probably better overall and I imagine most people will just get used to it, honestly.
It is a bit annoying having to make sure my nose doesn't get bonked when I drink, though.
I usually just breathe in as much as I can and hold my breath until I need another gasp of air. It usually goes away after two or three times.
Lying on your back and pressing your knees to your chest is another way to get them to stop that works for me.