Theoretically? Great idea.
Reality? They go bald after 30,000 miles or less, they're insanely expensive, you almost always have to replace at least two tires at a time, they can't be repaired like regular tires, they've got lousy road feel, they stink in winter conditions, and there's no way to tell which tire your car's low-tire-pressure indicator light is talking about, or whether the warning is real or fake, or whether the tire is going to suddenly give out altogether at an ungodly early hour of the morning, in the rain.
Since we attempt to make this something of a family-friendly blog, you will have to imagine for yourselves the Anglo-Saxon fricative curse words now queuing up in my brain.
Yes, there are class-action suits pending against the tire manufacturers.
In the meantime, it's our considered but non-expert opinion that regular tires plus a spare and a jack are the way to roll. If your tires go flat and you find yourself unable to change the tire yourself, you can get a Triple-A Plus membership that'll get you towed pretty much wherever you need to go.