The problem isn't the paneling, the problem is the structure to hold the paneling one mile up in the air. That is far, far larger than any structure we have ever built. They propose to hold it up by pressurizing the inside of the dome. Well, if you pressurized it at 1 psi more than atmospheric pressure, you would have a 16,815,854,700lb upward force. And I don't think 1 psi would come anywhere close to doing the job. Just think of how stiff a tire is if you inflate it to 1 psi.
The company claims the panel can withstand a 180 mile per hour wind, but that must be a panel with a specific surface area that is supported in a specific way. The forces on a dome of that size under wind loading would be astronomical.
And if you're inside a dome and there's a fire, and the dome starts to shrink, it would shrink towards the fire, in other words, towards you. This would be very, very bad. Men women and children running and screaming around with molten goo on them bad. Ever dripped candle wax on your hand on accident? What about burning plastic? Not good.