Note: I have a house rule in my game that says an active perception skill check has a minimum result of 1 better than a passive score. This is inspired by Torg where giving up your action to defend always results in at least +1 to your defenses.Passive skills are used when the DM wants to be sneaking about things the players/PCs wouldn't know about. Day three would not use passive perception. At that point they are actively looking for the goblins they know are coming and would be rolling their perception skill.
The ridiculous situation is created by passive skills just existing. The passive number is just an average of rolls over a long period of time, and would not at all be representative of what is happening at the time the goblins are sneaking in. It's a ridiculous situation from the very first time it is used, which is why I ditch passive skill checks.
Here we just disagree on a fundamental level. In my game a character keeping watch while the party sleeps isn't intently staring off into the distance like a sniper looking for a target for a solid block of time. They are awake when others are asleep, maybe doing a short patrol around the periphery, keeping the fire fed, mending a hole a sock, playing solitaire, or any number of other things. Their Passive Perception score is a level of "attention" they are able to pay to the world around them on a regular basis without switching to sniper targeting focus mode (which is an active Perception check in my mind).
I can't disagree more that Passive Perception is bad design, I think it's a good design to allow for characters to have a "normal" level of senses with a "heightened" level available in different circumstances.
You can try it yourself. Go outside and listen intensely to the sounds you hear. Pay hyper attention to each and every star, bug buzz, breeze, or smell. See how long you can do this before your brain says "I need a break" and you start thinking of candy bars or the Superb Owl or whatever.