Indeed it's quite possible to argue that of all the European powers the status quo ante bellum worked most to Britain's advantage. I'd argue it was in Britain's interests to maintain the armed peace and Grey should have intervened directly in the early stages of the crisis (proposing a great power conference in London to resolve "the Serbian Question" perhaps on the basis, as someone would claim later, jaw-jaw was better than war-war).
Which, in fact, Grey had done a little over a year previously, to resolve a previous Balkan crisis.
But given how sensitive this crisis was for one of the great powers, he obviously decided it was better to hang back.
Had he understood that the powers in Vienna had decided to use the crisis to completely crush the Serbian state, one would think he would have taken a much more assertive role. It *would* have been risky, of course, because both Britain and Russia would have to threaten war right up front to bring Austria (and Germany) to the negotiating table, and as you say, there were plenty of interests (mostly not in Britain) who preferred war. "We'll give you a generous mandate to punish the guilty parties - even in Belgrade - but the destruction of the Serbian state is going to be a bridge too far." That might not be an easy sell, but at least the major players would understand the stakes up front.
Obviously, the risk is that even if Grey did sell it, the risk was that it might just delay the explosion by another year or three.