His authority never came from action or decisiveness. It came from deliberation -- from taking moral questions seriously, visibly struggling with them, and arriving somewhere thoughtful. He could be shown uncertain, conflicted, or wrong without it undermining his standing. Most fictional leaders derive authority from what they do. Picard's came from how he reasoned.
That's an unusual model to put in front of a generation. The image of a powerful person treating an ethical dilemma as something worth the full weight of their attention is not common, in fiction or outside it.
A lot of people who grew up watching him internalized something they might not have had a name for at the time: that authority and genuine moral seriousness can be the same thing, not opposites.