I think a few of these, fritz, are examples of characters who stopped doing stuff precisely because no longer doing stuff was their arc conclusion. Homestuck cares a lot about the relationship characters have with the stories they're in, and it acknowledges that sometimes the best outcome for a person is to just stop participating in the narrative that's been crafted for them - that's basically the comic's ending summed up!

Sollux in particular is a strong example of this. When we meet him, he's living in a giant honeycomb tower, with honeycomb computers scattered all around; the subtle symbolism is that Sollux himself is just a bee in a great big machine. When he gets honey all over him, he stares down at his stained hands in a callback to Dave looking at the blood on his own hands; implicitly, the honey IS his blood, and it's the blood of lowblooded trolls like him that oils the great big Alternian machine. This is made as explicit as possible when we finally hear about his ancestor, who has LITERALLY been hooked into the machine of Alternian conquest. When the evil empire decides that from birth his entire purpose is to be a cog in a machine, the only way Sollux really can be happy in the end is to check out. After hearing the moans of doomed ghosts his whole life, compelling him to become the guy who invents Sburb, he finally gets to be a ghost himself and just sit in silence with his girlfriend for an eternity or two.

Davesprite I won't claim to understand so intimately. I've never really been hugely invested in his arc as a separate person from Dave, but I totally get why many of those who think of themselves as more Strider-inclined might have been disappointed. Personally I think it's interesting that, as a sprite, he's kind of SUPPOSED to stop doing stuff when the Reckoning sounds and the game ends. I really believe when he was sitting there on the Battlefield with Jadesprite, he was recognising that his purpose was over and intending to die! So by being saved at the last minute, he's left purposeless not just as an ancillary Dave but also as an NPC without a quest to give. In that sense I really liked the conclusion that he became an aspect of Davepeta, who kind of combines two pointless, aimless characters into one fully-rounded person who understands that their purpose is simply being who they are.

Arquius, meanwhile, is a great contrast to the above, because from the beginning we're never really supposed to NOT think he's a gag character? like, he's just a sillier version of Equius that makes Dirk uncomfortable (mostly by reflecting Dirk's nastier qualities back at him). So I can't see how he qualifies as a character whose potential was shown and then thrown... but the fun thing about Arquius is that he's possibly the premier example - maybe after Gamzee - of a joke character who was ultimately revealed to be a lot MORE important than they seemed. Because the end of Arquiusprite's arc is becoming (part of) Lord English! So by the time Arquius is gone, you're not meant to be left thinking 'huh, where did Arquius go, what did he ultimately amount to' - you're being invited to look back at all the times Lord English appeared in the comic, all the dastardly deeds that big hulking menace got up to, and wonder: just how did Arquius' personality factor into that? What is the significance of a little bit of Lil Hal and a little bit of Equius ending up as the story's main villain?