by Paul Nicholls.
Although I hesitate to suggest adding yet more settings, I wonder if this is perhaps a behaviour which ought to be configurable at the plugin/site level. Something along the lines of "Allow late submissions without a cut off date" - which would then allow for both cases presented here: wanting to allow late submissions by default (Richard), and wanting to allow them only when deliberately set (Madhusudan).
A single option at the plugin/site level would mean that each institution can set it in line with their expectations, though perhaps there would need to be some visible indicator in the assignment settings so that any teacher moving between Moodle instances can immediately tell which way it's set.