Squawk Ident has nothing to do with checking any altitude tolerance. Squawk Ident is to confirm the radar identification and produces a flashing circle, or similar symbol, on the aircraft label. The altitude appears on the radar so the controller can see it all the time but it is a requirement for pilots to report their altitude when requested so that ATC can validate the altitude read-out.
If ATC clears an aircraft to a different level it's up to the pilot when he complies. A level bust would not occur simply because the pilot was slow to leave a level.
Current controllers might offer other opinions?