Speaking as a 30 yr retired US controller, commercial pilot and flight instructor....
Several people here have seemed to imply that US controllers pass on all responsibility for separation to the pilots by issuing advance landing clearances. Nothing could be further from the truth. If separation doesn't exist when #2 crosses the threshold, the controller is still charged with an error, even if #2 had him in sight since they left Omaha. It becomes a shared responsibility, and allows the following crew some flexibility in adjusting spacing instead of forcing the controller to micro-manage every speed reduction. (Visual approaches) Regardless of the rules in use, I assume the crew of a following aircraft would use good judgment in assessing their spacing with the aircraft ahead.
Point #2, 50,000 flights per day, 18+ million per year, while no doubt the occasional misjudgment occurs, advance landing clearances are way, way down the list of potential hazards you'll face.
I did it for 30 years as a controller, been flying for 40 years, never been violated or had an issue at a towered field. If you want to see chaos try a fly-in BBQ on a nice Saturday at a non-towered field over here.....