I stay much warmer with the straps attached; they keep a slippery comforter like this in place (even around my feet). It's as warm as a sleeping bag, but significantly more comfortable.
I sleep in a Go Fast Camper using a GoWesty 1" mattress topper. The straps work perfectly under the topper.
Thanks for the great product, so much warmer than my previous down comforter (which was twice as thick!),
John