I think you have hit upon just the kind of character trait that makes a person "one after God's own heart". Since we know God says he is no respecter of persons, the same consideration he had for David can be for others, as well. It was because David was honest before the Lord, he acknowledged his failures instead of rationalizing them or justifying them and he wasn't too proud to prostrate himself flat on the floor in humble surrender to God. He loved the Lord, never doubted him and accepted whatever God brought into his life because he knew God loved him and wanted what was best for him.
Like you said, he was the King and all that that entailed including his every desire and need being met. When he did take that for granted and fell into sin, he repented - he named it as God named it - and he did not turn against the Lord when he reaped what he sowed. Even the king had to answer to one higher than him. We certainly can learn huge lessons from his life and that's how I know God is who is behind Holy Scripture. Men don't normally write about their failures and flaws but want to boast of all their accomplishments.
I just know I want to be a "woman after God's own heart". To be all that he wants me to be and do what he has placed me here on this earth to do all to his glory and praise.
Amen sister , that is my prayer too (for him to give a heart that is true to HIM)