My argument for this is that Vesuvius is over a dozen miles away from Pompeii, in clear sight. There should have been ample time to get away on foot.
What sounds most likely to me is that the explosion was powerful enough to instantaneously kill thousands of people in their homes, but this seems at odds with buildings and walls still remaining standing.
So what could have happened to those poor people that they were buried in ash in their own homes?
The term you are missing is pyroclastic flow. They comes very quickly, and you do not want to be in their way.
It should suffice to say that once the eruption happens, there's an exceedingly limited time to find shelter. It's not a gentle rain of ash from the sky you need to contend with, but a horizontal torrent.
Other information to keep in mind: Pompeii had released smoke before--no one had any idea that this time would be worse than any other time. Pickup up and leaving meant leaving your home unattended, and leaving your business. Also, with lots of people leaving at once, the roads were crowded. Some people stayed because they didn't want to leave their homes unattended; there were slaves who were chained up and couldn't leave; there was poison gas that overcame people, especially weak ones, there were people who couldn't leave because their health was bad, and there were people who were stubborn and wouldn't leave.