Redundancy in any aspect of dive gear is nice in principle, but in practice a question one might ask is whether the risk outweighs the hassle. Risk is sometimes defined as the combination of the probability of harm and the severity of the harm if it occurs.
The hassle here is having to own, transport, and maintain yet another first stage. Not a major hassle, but still, part of the beauty of recreational diving is its simplicity. The goal is to maximize fun while staying safe enough. "Self-reliance," as you mention, is good, but improving buddy procedures is the more standard way--that is, the way the major dive agencies teach--of dealing with problems. Before resorting to more gear, consider whether the kind of diving you do is amenable to improved buddy procedures. If what you are doing is more like solo diving than what the dive agencies classically consider "recreational" diving, then maybe take a course in solo diving and gear up like a solo diver.
How often do first stages (that have been properly maintained) fail in a way that suddenly cuts off your gas supply? I would say extremely rarely, unless you're diving in near-freezing conditions, in which case I would argue that much like the solo diving I mentioned above, you're no longer doing classic "recreational" diving; now you need to think more like a technical diver, and yes, that means redundant gear of some sort. You probably should NOT rely on a buddy for dealing with first stage freezes, because two divers breathing off the donor's first stage is likely to result in the donor's first stage freezing up as well. For redundancy, H-valves seem more popular in Europe, whereas ponies are more popular in the US.
Not in the UK, it's pony or doubles all the way.