@spawn goes into depth with some very principle story logic: Zoro isn't here to waste time.
1. He looks right past the All Stars when they're at their highest level of threat. Zero importance is given to fighting King as a task or desire.
2. Marco, the one who's fighting King, sees this. Marco's strength revolves around utility and stamina. Zoro doesn't ask for his help, he's the one who acknowledges that Zoro belongs in the main fight, and then boosts him straight up. Is he going to say, "glad you're back to health, now you can take over this fight I'm in! I may have the stamina but you guys have some similarities, after all "
3. When the elixir wears off, Zoro may be physically intact but will experience twice the pain of being crippled. He will be absolutely done fighting at that point. Why is he gonna bother with King? Flying around like that looks annoying as fuck.