I have always seen the argument of that because Super Saiyan 3 subverts expectations, it works in the story. And my response has always been the same: subverting expectations does not actually make the story better or more interesting. This is such a thing as bad swerves, and in my opinion, Super 3 is one of them.
If the theme that Toriyama was going for was that Super Saiyan 3 is a powerful transformation, but wouldn't be able to get the job done, that would have been fine. But the nature of which Toriyama approaches Super Saiyan 3 as a transformation to subvert your expectation is just so poorly done.
Piccolo point-blank asks Goku if he could defeat Majin Boo as a Super Saiyan 3, and Goku says it's very unlikely he would have been able to defeat Majin Boo. That's a good subversion for how Super Saiyan transformations are depicted as the be-all-end-all. But then, during the climactic battle against Kid Boo, Goku lets it slip that he could have defeated Majin Boo when he first confronted him and chose not because he wanted the new generation to handle the problem. This awful reveal absolutely undercuts any kind of subversive theme Toriyama may have initially intended with Super Saiyan 3.
If the main message of Super Saiyan 3 was that you should rely on the next more powerful transformation to solve the problem, that tidbit from Goku before he fights Kid Boo kills that kind of the message, because a transformation like Super Saiyan 3 would have resolved the issue, but it was because Goku not only chose not the resolve the problem -- a problem that he contributed to creating no less -- but he also chose to lie to Piccolo about the circumstances of the battle against Majin Boo -- which is horrendously out of character for him -- in a situation where he never previously alluded to the idea of wanting the new generation to learn to take care of themselves to justify not killing Majin Boo.
In terms of how much Super Saiyan 3 itself shakes up the narrative... it's barely noticeable. Goku displays Super Saiyan 3 once and then leaves, and everyone forgets about Super Saiyan 3 until Gotenks achieves the form (and how Gotenks was able to transform in Super Saiyan 3 is a mystery in itself), fucks around while using form against Super Boo. Gotenks achieving Super Saiyan 3 changes nothing about the dynamic in which Gotenks approaches his battle against Super Boo as he still retains his immaturity and desire for spectacle in combat over pragmatism. Which makes no sense because Gotenks already knows he working against the clock, so the audience isn't going to be fooled into thinking that Gotenks will kill Super Boo before the fusion expires. They've already seen how Gotenks fools around in battle, and his demeanour doesn't change even when Super Saiyan 3 comes into play and drastically shortens their time fused.
Hell, it would have been a better swerve if Gotenks actually killed Super Boo as Super Saiyan 3, given what context the narrative had provided for the circumstance of Super Saiyan 3 and Gotenks characterisation.
And it wasn't as if Gotenks burning out Super Saiyan 3 lead to the main cast having to drastically change their plans either, because Gohan was already training with the Zeta Sword and having his dormant power being unlocked while Gotenks as a Super Saiyan 3 was fighting Super Boo. It was Super Boo sensing Gohan's incredible power on Kaioshin's planet when Gohan powered up that served as more of a catalyst for moving the plot forward than Super Saiyan 3 Gotenks being a thing.
As mentioned before, it's only during the final battle that Super Saiyan 3 gives any foundation for coherent and good writing as it provides some of the foundation for Vegeta's epiphany in the climactic battle against Kid Boo. But even during that conflict, Super Saiyan 3 burning out against Kid Boo falls flat as a swerve given that:
a) It's already established Super Saiyan 3 is taxing on a mortal body
b) The form has already proven to be ineffective against Majin Boo twice
And the whole "The humans need the learn to fight for themselves" message is horribly shoehorned in when you take into consideration that either Gotenks or Gohan could have been brought to Kaioshin's planet to fighting and easily Kid Boo. And how their inclusion in the final battle would have better served the main narrative theme a good chunk of the Majin Boo arc had revolved around: the new generation fighting their own battles. I mean, don't you think getting another crack at the whip against Majin Boo could have served as a great avenue for the character development Gotenks desperately needed and the personal resolution Gohan seemingly never got?
The good that Super Saiyan 3 brings to the table narrative-wise, is vastly outweighed by the bad. Mostly due to how haphazardly the form is integrated into the plot. It leads to bad swerves, zero character development concerning the characters it's used on, undercutting the major narrative theme which the arc was going for (the new generation need to learn how to fight on their own) in favour of a last-minute narrative that had no build-up in the arc it's introduced in.