Actually, the whole family wasn't home. Three of the five children/step children were home. There were powerful connections, sort of. Percy himself had no power other than being a successful businessman, which was far from unusual in Kenilworth. He had lost the only election he'd run in. He certainly had connections in the GOP, for what it's worth.
But he said if he lost the election that he was in at the time, he would have quit politics, and we know there was a sympathy vote of one percentage or another that helped him on the election day. The cops actually knew where the family was when they left. Campaign staffers put themselves between the family and the cops. The local cops or Chief apparently permitted or tolerated this to some degree, to the chagrin of at least on Chicago detective, perhaps because of their inexperience or inexperience having the national news media cover their every move.
Dr. Hohf was miffed at being excluded from coroner's inquest and wrote that things seemed weird in the house. But, judging from his account of that day, written a few days later, which is otherwise excellent, it appears he seriously underestimated the time that he snoozed after waking up initially and getting Percy's phone call. It may have been stated here previously but it was enough time for at least one, if not two, cops to arrive, the Winnetka Fire Dept to get to the house (and perhaps leave.)
I suspect two cops were there before Hohf (he even mentioned this), which allowed Wolf to escort Hohf back to Percy's house, which means Roddy, the second cop to arrive at Percy's that day, had to be relieved at his post at the police station by the Chief. So it may have been a half hour or so before Hohf was there (Roddy also chased a motorcyclist and pulled him over for a minute or two beforehand.)
IMHO there's little reason to doubt the bayonet was the weapon. So as I may have said before, 16 inch old military knife, intruder smashes his way into home, dozens of investigators work full time and turn up no likely suspect. Sounds like a random psycho to me.