Well, Garnet and Amethyst did do exactly that, immediately after they discovered Jasper was still alive in "Alone at Sea", while Pearl, Connie, and Steven went north to hunt Gem Monsters (and inadvertently ran into Jasper). And at that point all the characters continued to look for her until this latest Jasper arc was resolved in "Earthlings", didn't they? I don't need to defend the show, and I know that everyone's got preferences when it comes to storytelling, and maybe I don't understand precisely what you mean... but doesn't that fit the bill?
If you're mad they took so long to bring Jasper back after she fell out of the plot, and into a magma-filled chasm split down to the core of the Earth, I get you. Consider this, though. From the characters perspective Jasper was destroyed, trapped underground, or otherwise gone. From the writers perspective, they want to keep the plot fresh, and not linger on one conflict (Malachite/Jasper) or Jasper's story overlong, and neglect all the other plots going on. Peridot still needed to wrap up her redemption arc, Lapis needed to deal with the emotional aftermath of their fusion, Steven needed to figure out why Jasper (and Homeworld) hated his Mom, etc.
Anyway, I was looking forward to a Jasper redemption arc too. The Crystal Gem team needs a gigantic orange emotionally-inept butch space rock who secretly just wants friends, IMO. But we may not see that for a while, when/if Steven figures out how to cure Corrupted Gems or something... and I have a feeling that's a long-term plot.