For example, tires lose air on a daily basis and have to be pumped up. Additionally, even the best pumps require a bunch of fidding to attach and detach the hose to the air fitting.
Tires and suspension are a tradeoff between comfort and efficiency. Lower rolling resistance means a stiffer/harsher ride. High pressure tires are narrow, have a very small contact patch and no "suspension travel"
Even though it's cliche, I think reinventing the wheel might take us interesting places.
It's also limited by the tubes and/or patches you've brought with you. If you blow a tube, you should have a spare. If you lose a second tube, you may be out of luck. Maybe it can be patched, though I've found patching unreliable. You may be in for a long walk, in your cycling shoes -- especially if you've ridden out of cell phone range.
These are clearly going to be far beyond the price point of your casual rider, at least for a while. But if they can match the ride experience, and eventually lower the price, I could see these being wildly popular.
Pneumatic tires are hard to beat, but there's a lot of room for improvement in their durability. Which is really important for something you depend on so much.