If there is a birdstrike, then I pass the information, let arrivals decide and get an inspection as soon as possible. We do not depart an aircraft until there has been an inspection (With the exception of someone already lined up, I may launch them with information if I feel they cannot vacate before a G/A).
As far as debris goes, if an aircraft lands with structural faults or aborts with structral issues then we dont use the runway without an inspection, certainly not for departures. If I think its big debris or close enough to the runway to cause an issue, I'll instigate a G/A. I have no issues in justifying it on safety grounds. If a G/A will comprise the flight, then you should really have mentioned it earlier or of course you retain the right to land anyway...
