Just as you know that I'm not suddenly going to hate that ROTJ sequence after all these years, I know that you're not going to suddenly be as okay with it as I am. But I can try to explain why I see Fett's goals in that scene being reason for him to have very limited opportunity to be a badass in that scenario. Plus, I like imagining Wor-Gar rolling his eyes into the back of his head when I post SW justifications, so here goes.
If I was Fett, and I had already collected my Solo bounty from Jabba, I wouldn't give a crap about Han escaping. It might just increase the next bounty on him anyway if he were to get away alive. So what's Fett's goal in that moment? Well, seeing he knew how badly Vader wanted the Skywalker kid, who happens to be standing right there in danger of being killed by Jabba goons, taking him captive and delivered to Vader is the only thing that makes sense for bothering to get involved.
Fett knows Luke's value is in being taken *alive* (hence the elaborate carbonite plan). That's why his errant rifle aim before Luke slices it is fine with me. And when he shoots his gauntlet missiles, it again wouldn't make sense to hit Luke; but maybe hit the lightsaber (a very elusive and difficult target) to disarm him. He also resorts to the lasso rather than using his flamethrower or darts, and that logic works too. Needing to focus on the Jedi he's trying to wrangle, a freak accident happens when he's not paying attention to Han. Certainly not what I wanted, but it's not devastating to me either. Fett's badass reputation is clear enough anyway that I don't feel seeing it displayed on screen would've exceeded what was already in my imagination from his mysterious past.
And while I no longer accept the PT as background lore, you *do* (at least to some extent), so there's an extra bit of context for you regarding Boba's role in that skirmish. If he saw Mace decapitate Jango, then it stands to reason that Boba would have a vendetta against Jedi. And who better to attract Vader's attention for tracking and capturing surviving Jedi after Order 66 than Boba Fett? With Luke, he had a chance at one more big Jedi capture payday. But he's just not as good taking them alive.