tl;dr– Simpson's paradox isn't problematic unless correlations are inappropriately assumed to be causative.
Background: Simpson's paradox only happens when causation was fallaciously assumed.
Let's suppose these premises:
Healthcare can help apparently-healthy people.
Healthcare can help apparently-not-healthy people.
People receiving healthcare are more likely to be apparently-not-healthy.
Here we have an opportunity for Simpson's paradox: the bulk population has a negative association between apparent-health and receiving healthcare, despite each of the two sub-populations having a positive association.
But it's not really paradoxical (confusing), right? I mean, obviously, the negative association is due to people seeking medical attention when they're apparently-not-healthy.
The missing component is assuming causation. For example, if someone does a study on the correlation between apparent-health and receiving-healthcare, then assumes it causative, then they'd perceive a paradoxical situation in which:
Healthcare helps healthy people.
Healthcare helps not-healthy people.
Healthcare hurts (healthy OR not-healthy) people.
Absent false presumptions of causation, Simpson's paradox isn't a paradox.
How to handle Simpson's paradox?
Same thing you do when you discover that $1 = 2 :$ realize that someone messed up along the way.
To be clear, a legitimate analysis can find correlations in which the total population has a different correlation than its component sub-populations, such as in the example above. But a legitimate analysis shouldn't be able to arrive at a situation where causative behavior is reversed.