Could a controller or airport in the US decide to use English-style landing clearances? In the U.S., controllers are allowed to clear multiple planes to land on the same runway, with the assumption that the first plane to land will be out of the way by the time the second plane gets there. However, in England (and I think a lot of other places), you're not allowed to clear a plane for landing until it's the very next plane to land and there are no takeoffs or crossings ahead of it.

Could an American controller, or airport as a whole, just decide not to do sequenced clearances? That is, if they need to cross a plane in front of one that's landing, tell the landing plane "Cancel landing clearance but continue approach", then re-clear them to land once the runway is clear?
The use of FAA's anticipated separation rule is theoretically optional, and there are indeed times when controllers don't use it. While not common, now and then one hears "continue approach" (or similar) instead of an early landing clearance, as is normal under ICAO rules. Ditto for the occasional canceled clearance.

However, anticipated separation exists for a reason, and a trainee who was unwilling or unable to use it when appropriate would not pass. OTOH, they also have to know when it's not appropriate and not use it at those times.