Actually, it is scriptural. Daniel 9 is the most often referenced example.
I have to admit, I get resentful and tired of doing it, especially when I haven't personally prepared for it by doing the historical research. But it is scriptural, and it does break the enemy's power and open doors to reconciliation- which is where the Holy Spirit shows up and reveals Jesus to people that don't know Him.
It may not have much of a political effect, but it's spiritually very potent in the lives of individuals- some of whom may be politicians.
God’s punishment was being bestowed upon the Israelites for sins Daniel and the others had been committing (”All Israel has transgressed your law and turned away, refusing to obey you.”—Daniel 9:11). Daniel, in his unique leadership position, was explicitly made responsible for the people he represented before God, the Israelites.
There is no person on earth who represents and is held accountable for God’s people who are Christians. As you can tell, there are over 100 people who, at the most, can only represent themselves and the congregations they lead. They can’t represent people for the following:
“...we want to begin by acknowledging that in the past (e.g. in the Crusades) and in the present (e.g. in excesses of the “war on terror”) many Christians have been guilty of sinning against our Muslim neighbours. Before we “shake your hand” in responding to your letter, we ask forgiveness of the All-Merciful One and of the Muslim community around the world.”
These people have no authority to ask for forgiveness of the sins other people did before them.