To be fair @ATerrorofLeftovers, it is something that can and does happen, though I don't know why it happens for some patients and not others.
I can't take propranolol and I refuse SSRIs or antipsychotics, and currently get benzos on a repeat prescription, to use whenever I want, for sleep/agitation/anxiety/whatever. Only 14 x 1mg lorazepam (at the moment — a while back it was 28, but I wasn't using anywhere close to that), so little to no chance of forming actual dependency, and most months I don't request any.
I've never had any trouble being given benzos if I request them, and never developed a habit. If offered z-drugs, I ask for benzos instead and there's never a problem. GP out-of-hours once happily gave me a full box of 5mg diazepam for anxiety/agitation, while someone I knew would be lucky to get 2 x 2mg. Going through a bad spell, an emergency GP told me to take 5mg diazepam 4 times a day for two weeks, and when that didn't work, I attended a drop-in clinic in another county who added 1mg lorazepam, same schedule, same duration, to take on top. Crisis team gave me clonazepam to take on a similar schedule, when I refused antipsychotics, which I reluctantly took. It's not a class of drugs I've ever experienced any reluctance to prescribe from doctors.
I guess either I've just happened to always come across less wary doctors, or there's some sort of individual or illness characteristics that affect whether doctors are happy to prescribe this way for you.