What is the ruling of Islamic law regarding the action of the two friends who left the imam praying alone to pray in congregation, thinking it was better to catch the opening takbir, and is this permissible?

The action of the two truthful ones (al-Siddiqayn) in falling behind the congregational prayer due to missing the opening takbir indicates their lack of knowledge. They should have joined the prayer to increase the congregation, based on the Prophet's (peace be upon him) saying: "Indeed, a man's prayer with another man is purer than his prayer alone, and his prayer with two men is purer than his prayer with one man. And whatever is more numerous is more beloved to Allah Almighty." Thus, increasing the congregation is more emphasized than catching the opening takbir, especially since the narrations regarding the virtue of the opening takbir are not free from weakness in their chains of transmission.