At Lagos (for example) the debris could be human
In general, I agree with the philosophy of telling us the pertinent information and let us decide. As others have said, it may be that a greater problem would arise by going around than by landing. Personally I would also land for bird/small animal remains and use idle reverse; tyre debris / aircraft bits fallen off, it would depend on where they were - anything over 2300 metres from the threshhold would probably result in me landing [B747-400], anything significant before then, a go-around.
As you can see, there is no simple answer as multiple factors come into play - I commend the approach of telling us all available information and letting us decide - that's what we are there for, and we have information available to us re our performance/endurance that you don't; if you say 'go-around' we have no option, really.