Could a controller or airport in the US decide to use English-style landing clearances?
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.