What's with the ridiculous scenario? The most "bloodlust" Goku ever got was when Krillin died after Piccolo "died". So, just getting Gohan or Chichi killed or tortured is more than enough to give Goku the bloodlust you want. You really don't need to go through all the silly details about ripping their arms off and whatnot.
Okay, that's besides the point. And let's take a look at what "bloodlust" really does in DBZ. Gohan, when fighting Frieza, was bloodlusted and got a huge boost in power. He also did the same against Raditz and Nappa. But that last like...one blast, or two, and then Gohan was totally out of juice. As for Vegeta, you can use that PIS from the movie, which I label as total BS. But that doesn't really demonstrate how strong Vegeta got as Beerus' power fluctuated a lot. He seems to use just enough to overpower his opponents. Besides that, Vegeta's other bloodlusted scenes mainly consist him going crazy and spamming ki blasts. Now for Goku, I mentioned it already. Goku's most bloodlusted scene is when Krillin died and he went Super Saiyan because it Super Saiyan required anger to fuel it.
Bloodlusted or not, it's not going to do much unless it allows Goku to achieve Super Saiyan 2. The other 2-3 forms of Super Saiyan were achieved through hardcore training and not really "anger" like how Super Saiyan 2 was. The most you'll get out of a "bloodlusted" Goku is a barrage of amped melee attacks or ki blasts. And that's it. It's not even going to last more than 1 minute in DBZ time frames (remember how the Frieza battle took like 5 episodes for 20 minutes or something like that?).
Now if you look at how strong Goku is at that time, he's around the same level as Vegeta. Even if I give you that Goku is stronger, it's not by much. Both Android 17/18 are considerably stronger than 19/20 and Vegeta/Trunks by a large margin. It's like Perfect Cell vs Vegeta before the Cell Games and Cell was just stomping Vegeta. That's basically what happened with 18 and Vegeta too. He wasn't just beaten but stomped.
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