I'm not going to go into why Jean Smart left the show (https://www.sitcomsonline.com/boards/showthread.php?t=13013) in Season 6 along with Delta Burke, because it has been addressed on her already. As for Carlene, why did that character have to be made out to be Charlene's sister? Apparently, when Charlene was very vocal about her family in early seasons, with no mention of Carlene. And even when Charlene's family made an appearance, there was no sign of Carlene. To be more specific, in a Season 1 episode where all of Charlene's family visits, she goes around the room and introduces them to Julia, Suzanne, Mary Jo and Anthony. Charlene's sisters were Darlene, Marlene and Harlene. There was no Carlene. And on the same token, Carlene rarely mentioned Charlene and when she did, it just always came off as awkward for some reason.

Had Delta Burke not left (and she Annie Potts and Dixie Carter continued in their roles), would we not have had Jan Hooks as a replacement to Jean Smart? I mean, because Suzanne going was such a loss and they went with a completely different character (in Julia Duffy's Alison), did they have to try to clone Charlene (the "innocent and fun-loving one") to keep the dynamic the same?

The introduction of Carlene Dobber (Jan Hooks) is widely regarded by fans and critics as a major continuity failure and a symptom of the show's struggling identity in its final years.

The "Ghost Sister" Continuity Error
You are correct that Carlene's existence contradicts years of established lore.

The Missing Name: In the Season 1 episode "Nashville Bound," Charlene explicitly lists her three sisters as Darlene, Marlene, and Harlene.

Production Choice: Creator Linda Bloodworth-Thomason reportedly chose to "create her from scratch" for the Season 6 premiere rather than using one of the established names, a move that remains a "major sticking point" for the fanbase.

Lack of Resonance: Because she was never mentioned during Charlene’s many family stories, her sudden arrival as a "favorite sister" felt unearned and awkward.

The "Clone" Strategy
After losing two original leads, the producers intentionally tried to replicate the show's successful "four voices" rather than innovating.

Voices, Not Characters: Bloodworth-Thomason admitted that while Jan Hooks and Julia Duffy brought their own personalities, they were essentially playing the "voices" of their predecessors.

Carlene vs. Charlene: Carlene was designed as a younger, "hickier" version of Charlene—a "female Woody Harrelson" who lacked the original's sophisticated growth.
Allison vs. Suzanne: Similarly, Julia Duffy’s Allison was cast to fill the "antagonist" slot, though her "Obnoxious Personality Disorder" was far more abrasive than Suzanne’s oblivious vanity.

Would Jan Hooks have joined if Delta Burke stayed?
It is highly unlikely.

Reactionary Casting: The hiring of Jan Hooks and Julia Duffy was a direct response to the mass exodus of Smart and Burke at the end of Season 5.

The Smart/Hooks Connection: Jan Hooks was hired specifically to replace Jean Smart, who wanted to "ease herself out" to spend time with her family. Had Delta Burke stayed, the show would likely have only looked for a single replacement (or a new partner) rather than the "re-design" that occurred in Season 6.