Re: High speed tires
....guys riding skinny road bicycles in the Tour de France regularly hit 50-60 MPH on the downhill mountain stretches.
....people who ride MTB's down ski slopes in the summer regularly hit 70+.
A few years back there was also a guy who built a fully-faired recumbent and put a 2HP engine on it, and could get up to like 65 MPH or so. I don't remember his name or know what kind of wheels & tires he had.
I would guess that what would fail at high speeds would be the tread belt coming off the tire,,, but that wouldn't happen all at once. It would start in one spot, and you would feel it. When it happens on cars and trucks you can feel it.
Really though a tire is only one part of a whole bike.
If you're starting out with the cheapest bike and parts around, I wouldn't expect it to be very safe beyond 25 or 30 MPH anyway--and even that would only be on VERY smooth roads.