I know it varies by situation. When I've been on call I've been able to mostly go about my life. I just had to keep my laptop close, stay in cell signal, and accept I would sometimes have interruptions (typically brief). We fought to keep them infrequent enough that they didn't ruin our lives.
If I want to go meet a friend for a drink or food, I have to lug around a backpack, keep an eye on it to make sure it's not stolen. If I wanted to have a beer or wine, I can't because I may need to work at any point.
Favourite band is performing? I suppose you could take a backpack and the laptop to the venue, but again there's a chance it's pinched, and they'll make you check it at the cloakroom for the performance.
One beer or glass of wine renders you incapable? I'd be totally comfortable having 1-2 drinks on call.
If this is a stated requirement from your employer, talk to a lawyer. This is a common litmus test for whether you need to be paid while on call, even if you aren't actively working. Depending on the jurisdiction you may be entitled to pay (or trigger a relaxation of your company's policies).