In practice the only time I've ever heard of something like that bite are serious firmware bugs (i.e. a counter overflow causing drives to cycle after 45 days of uptime - source: I work for a major CDN with a six figure drive count).

There are some statistical properties I recall that will make mechanical failures spread somewhat nicely, maybe someone can elaborate if they have a background in stats.

I've seen it. RAID5 with 5 similar disks failed during weekend. All but one drive were dead. Of course disk failure also prevented daily backup run and all hell broke loose on Monday morning. The exact reason of death is unknown. Important fact is that the raid was configured on Thursday. So I guess the same time death is most probable when drives are really new and from same batch.

I saw that once in an array that was on 24/7 for years. 1 drive was failing so they shut it down to replace the drive (perhaps hot swap was not an option?) and almost all of the rest of the drives did not come up. Basically the heads stuck to the platters. Aka "stiction".

I would guess in your scenario something like that happened. Or perhaps trying to migrate tons of data to a new disk caused an issue. Just seems unlikely otherwise.

Yes, there is a concern in getting a bad batch, or having several drives fail all at once. Interestingly enough, while opening those 1450 anti-static cases and seeing the manufacture date of them, they were in separate batches (some with more dust on the cases than others), so we have some heterogeneous-ness on them. HDFS with its various levels of replication factors, and our backups/DR for high-value data takes care of the rest.