Are we discussing this assuming that primogeniture was the basis of sucession, I don't think that was the case, it certainly was a factor, but the reigning king and/or the nobles/guilds effectively decided to project a particular prince based on his abilities, certainly factors as mothers nationality would have come into play.
Even the sone of Nandivarman III had the problem. Nripathunga was from a Rashtrakuta queen and Adithya was from a native queen.
Laws of succession are complex. For example Agnatic primogeniture is inheritance by the first-born male child. Cognatic primogeniture is inheritance by the first-born child without regards to gender.
Take the case of Kulottunga I, I am sure there would have other royal princlings who had paternal claim to the throne, still Kulottunga was chosen. Which is against the Salic law followed by French this law forbade any inheritance of a crown through the female line.
On the whole I believe Chozha system of choosing the ablest or the most suitable prince out of the pool was better than the rest.