@Matou38. So sorry to hear about what happened to your poor boy. Having dealt with dog attacks myself, I know how violent they are; it usually takes me several days just to get over the shock. As for the police, I'm not surprised—a formal complaint means paperwork and follow-up, which they often try to avoid. The law states that if someone wants to press charges, the officer must take the report, but in practice, I've seen a policewoman talk a man out of reporting a breach of a child custody order (he'd come to pick up his daughter for the weekend and the ex refused), which is just awful...
Six months ago, a hunting dog on the other side of the road spotted my friend's dog. He started barking and lunging on the lead, the clip snapped, and instead of going for the dog, he bit my boyfriend on the arm and wouldn't let go. My friend had to go to A&E—his arm was full of holes and was swollen for a week. The officer he spoke to refused to take a formal statement, even though a person had been bitten, saying the injury wasn't "serious" and it was just an accident (!). They just logged it as an incident. My boyfriend went to the local council to report it, and they said, "Oh, nothing's been reported to us, we'll let you know." We're still waiting.
Take care of your lad, and make sure there's no lasting trauma by continuing to walk him with other well-socialised dogs. Have you checked your home insurance? It usually includes public liability cover which might cover the vet bills, or at least help in dealing with the Staffie's owner and their insurance.
As you said, the dog could have bitten you in the heat of the moment, or a child who happened to be in the way. The owner is being completely reckless if he knows his dog has issues; he should be using a muzzle for everyone’s safety (regardless of whether the dog is a pedigree or not) and working with a dog trainer. If there’s an incident, it’s the dog that pays the price—behavioural assessments, being seized, the pound, the rescue centre, or even being put down... that’s what's waiting for him.
Did you get an incident log or a crime reference number? If not, I think I’d head back to the police station and insist. Like Kikaah said, send a recorded delivery letter to the Staffie owner demanding they reimburse you (as you said, not for the money, but for the principle of it—you have to hit them where it hurts, in the pocket). You might also have legal expenses cover with your insurance. Hopefully, this incident serves as a lesson to that young man; who knows how he treated the dog afterwards or what he might do next... But a Baskerville muzzle isn't an "optional" extra; the dog can still eat, drink, and run in one, but he can't hurt anyone. You have to own it in front of others and explain why he's wearing it, which isn't easy, but I’d much rather do that than put someone at risk or put my dog’s life in danger.