On the whole, I agree with you, people shouldn't get the benefits of marriage without being married. But I think widowed parents allowance is different, it's for children.
Our benefit system counts couples as couples when they are claiming for tax credits if they live together, so I can't see why they can't do it for this. It's not a benefit that is open to any abuse, it's a tiny tiny proportion of the overall benefits bill, and people understandably, genuinely, need it when their spouse has just died and they and their children are in shock and grieving. I think it would be fair to means test it and withhold it where there has been a big insurance payout, but that's unlikely to happen where a couple are unmarried anyway.
Other than child benefit, bereavement benefits like this are the only ones I've ever claimed, and I find it very hard to stomach that anyone would begrudge a family such a small amount of state help at a time when they are in extreme and awful circumstances.