Re battery-draining radio broadcast
I leave BT on all the time, and have done for years with my current iPhone SE and my previous HTC One S, simply so that I can use it hands-free in my car without any messing. I've tested both phones to see how much difference it makes to the battery life and the answer is not a lot, in fact no noticeable difference at all, unlike GPS and (on the HTC only), WiFi. If I don't make any calls or use the phone for anything else during the day, but leave BT on, the iPhone uses <10% of its battery.
I used the HTC for 6 years and its battery was still fine for a heavy day's use when I reluctantly abandoned it in favour of a 'new-fangled' phone with 4G mobile and 5GHz WiFi so I suspect that if BT flattens your battery with a day's use, it's probably time you bought a new battery or a better phone!