Your health data could be used in the future, when technology is more advanced, to infer things about you that we don't even know about, and target you or your family for it.
I think in the US, you get out of the system what you put into it - specific queries and concerns with as much background as you can muster for your doctor. You have to own the initiative to get your reactive medical provider to help.
Using your own AI subscription to analyze your own data seems like immense ROI versus a distant theoretical risk.