Merseyrail used to do that as fairly normal practice, though in light of recent issues I imagine they are now much stricter.
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The difference between flights and trains is that for the former, a cut-off time is clearly advertised and printed on your boarding card (in easyJet's case, far more prominently than the pushback time), and flight boarding near enough never occurs in advance of that time so there is plenty of leeway.
With trains, only one time is advertised, and that is the departure time. Therefore, some confusion is probably understandable - though "30 seconds before" and "2 minutes before" is now much more prominent than it was, I personally think the public timetable should be changed so the time given at any given station is the end of the permissible boarding time, i.e. the doors close button is not pressed until the time ticks over to the specified minute.