We had a DST on our first kill on week one, gave it to a rogue who had helped gear our main tank. 2nd one dropped last week in our alt/pug run, it went to our guilds Warrior tank because the only other main in the raid was the rogue who already had it. I mean based on my actual TBC luck that's a lot better already, and I've seen some guilds with multiple hunters/warriors/rogues running DST but It's a cursed item and I wouldn't be surprised if I never loot it, for a 2nd time.
In the original TBC I remember the trinkets never dropping, whether it be DST, Tsunami Talisman or Madness. I didn't even see a DST drop and only one Tsunami/Madness. So I used Hourglass of the Unraveller + Shard of Contempt in Sunwell. I remember not liking on-use trinkets back then, these days I'd have used Bloodlust Brooch.
But this BIS within a tier thing just wasn't a thing back then, at least not before T6, largely because it was a ladder you climbed and you probably had a bunch of T4 stuff equipped while progressing T6, I definitely did.