Back to the ATCO possible ways of dealing with this situation, a few weeks ago we had a birdstrike (to the fuselage) crossing the threshold for landing. I reported it ASAP and tower asked the next plane if they had copied the info and if they where happy to continue, which they did. AFTER this plane landed all others were vectored for the other RWY as the one we (and the plane following) had used was closed.
I feel giving the option to the crew is better than suddenly instructing a go around (if not REALLY required). The crew might still elect to go around but would have some time to prepare. A few seconds is more than enough to highly improve the chances of the Go Around being flown as they are supposed to be flown. IMHO.