Only one lineage?

[Legolas]

I simply cannot see any reason why Elrond's children should be favored over Elros' when both are, by nature equally mortal. Clearly the privilege of choice was related to their descend from Earendil and Elwing and should apply to Elros' descendants as well.

Because Elrond's children were the result of the marraige of two immortal beings.

Manwe deemed it important enough that the children have the choice to stick with their parents to extend that right to them.

Elros left the world, and so did his wife.

You can disagree with Manwe (and Eru, or even Tolkien), but that doesn't change their motives or reasoning.