That's not true actually for birdstrikes. The vast majority of birdstrikes which involve engines only involve one. To involve all four is actually pretty rare, because it needs to be a pretty big flock of birds to cover the distance between a 747's no. 1 and no. 4 engine - involving both on a twin is actually a lot more common, as a smaller flock can straddle both engines. Modelling has shown that <10% of occasions of a four engined-plane passing through a flock of geese will all four engines be involved, and real life data supported the model when analysed. The mode was 1, and the median was between 1 and 2 I think).

There's never been a modern day commercial four engined jet taken down by birds - the last four engined jet to be lost was an AWACs (modified 707), and that did not involve all engines, but rather occured at a critical phase of flight. The data shows that generally, four-engined aircraft are safer from birdstrike risk, such that at some airports with extreme hazards, airlines have adopted policy of only using 4-engined aircraft.

Where it isn't a factor is in transpacific ETOPs - the highest recorded birdstrike was at 39000 (with a rumour of one at 48000! ) - but the vast majority of strikes occur below 2000. Out over the Pacific, you'd need a minor miracle to hit anything at cruise altitude, because it is not a migratory route (strikes above 2000 feet tend to involve birds which are on migration). At the same time, I used the incident to show that there have been incidents when a couple of extra engines on the plane would have been nice to have!