Bloodrazor...Is It Worth It?

Few things: firstly, Blade of the Ruined King is 6% of CURRENT hit points, not maximum. That's a crucial difference in any analysis. Additionally, one costs 1000 gold less than the other, which you have to take into comparison.

Also, at 2000 hit points, you're looking at 60 damage and 10% cooldown from Warrior vs. 60 damage + 40% attack speed for Bloodrazor based on the numbers from that patch. Warrior is definitely stronger in the early-game, but Bloodrazor edges it out easily against pretty much all opponents in the late game. It's worst case scenario against a 1600 health late-game target is still 48 damage and 40% attack speed, which is really powerful comparatively on anything without huge AD ratios -- and those characters will definitely be buying Warrior instead.

You are correct that you can sit on it for a while though. It comes online as a powerful item for cost in the mid-late game, but it's early game is, I believe, mediocre. I also wouldn't recommend it on ANY champion who builds Nashor's Tooth: there's not actually much synergy there, since Nashor's users will typically just want more AP.

Your overall analysis could have used clarification: items don't HAVE to be strong on their own. I'd have suggested changing the analysis to "On most champions this item isn't particularly powerful as a rush unless you're exclusively looking for % health damage to take down tanks or jungle monsters. If you want a strong early game jungle item, consider Warrior instead. Bloodrazor DOES, however, earn its keep as a second or third major item, as it's fairly cost efficient, and the attack speed it provides can really help bolster an early AD purchase or a Blade of the Ruined King."