If your choices are "use Jira" vs. "build task management software with an LLM" then you are already in a losing proposition. Go spend some time with Redmine before building your own. Redmine is free, far better than Jira, and already includes the features you don't yet realize you need.
Yeah, it’s a false dichotomy. Ironically, even in the advent of LLMs very little has changed here. An off the shelf solution to a problem has always usually been better than building it yourself most of the time. People just think it’s easier to build now, and it is. But that doesn’t mean it’s the efficient choice.