I thought that suspect bird strike events were covered by the FCOM and based on specifics of equipment type and experience. Generalizations are never going to cover subjective judgements.
This thread could probably go further if the question was about a specfic equipment type (including engines) along with the applicable FCOM paragraphs.
As far as mandatory reporting, this catch-all is also subjective. Most bird strikes go unreported because the symptoms are not overt and the pilots don't take the time to write up "might-haves". Where symptoms are involved requiring actions most of these strikes are reported by the crew. Many evidences of strikes are found on the ground after the flight. Thus the issue to me is crew response to symptoms and not necessaily bird caused.