I remember Keenan Lewis made a statement awhile back (years before Payton stepped down) saying that DA didn't have the right people skills. Maybe there's some truth to that.
Without being unkind or uncharitable, it would be hard to watch DA's press conferences or post-game speeches and not gather immediately that he is not a charismatic leader of men with abnormally high people skills. The way he carried himself also did not match what you tend to see from successful HCs, though obviously there are all sorts of outliers.
SP had obvious flaws and deficiencies too, but he looked and acted like a football coach that people follow into a fight, in the same way Brees carried himself as a platoon leader who'd outwork his own soldiers and put himself first in the line of danger.
One of the things that's been difficult the past couple years is both DA and DC not having personalities that mesh with fan expectations of what they want to see in a team they believe in. Doesn't mean they aren't great people outside of the team or not world-class talented. It's just their affect makes people much harder on them.