It is not that simple, because a large part of the genes that originally belonged to the mitochondria or to the chloroplasts have been transferred into the nucleus and they are now completely integrated into it, even if evolution trees will show that those genes have a different history than the remainder of the nucleus.
So even if you want to use only the DNA inside the nucleus for a cladistic classification, that does not produce a tree of evolution, but only a directed graph of genetic information flows, with many important hybridization events. While initially mitochondria and chloroplasts were just symbionts, like the useful bacteria in the human gut, eventually that symbiosis has become a full hybridization, with mixing and integration of the genetic information.
The official cladistic classification produces a tree from the directed graph of the evolution by cutting the branches that are considered to be less important.
Sometimes this is indeed the best choice, but there are contexts in which the genetic information brought through the minor branches is actually that which determines most of the importance of an organism in an ecosystem.
E.g. in many contexts the most important feature of a living being is whether it is an oxygenic phototroph due to inheriting genetic information from some blue-green algae, i.e. that it is a primary producer in the ecosystem, and not the features that depend on which is the exact eukaryotic group from which most of its nucleus has been inherited. For instance, it is more frequently useful to group together brown algae with red algae (whose chloroplasts share a common ancestor), than to group brown algae with some non-phototrophic stramenopiles (which share a common ancestor for most of the nuclear DNA), with which they share only inherited characters that need an electron microscope for detection.
So even if you want to use only the DNA inside the nucleus for a cladistic classification, that does not produce a tree of evolution, but only a directed graph of genetic information flows, with many important hybridization events. While initially mitochondria and chloroplasts were just symbionts, like the useful bacteria in the human gut, eventually that symbiosis has become a full hybridization, with mixing and integration of the genetic information.
The official cladistic classification produces a tree from the directed graph of the evolution by cutting the branches that are considered to be less important.
Sometimes this is indeed the best choice, but there are contexts in which the genetic information brought through the minor branches is actually that which determines most of the importance of an organism in an ecosystem.
E.g. in many contexts the most important feature of a living being is whether it is an oxygenic phototroph due to inheriting genetic information from some blue-green algae, i.e. that it is a primary producer in the ecosystem, and not the features that depend on which is the exact eukaryotic group from which most of its nucleus has been inherited. For instance, it is more frequently useful to group together brown algae with red algae (whose chloroplasts share a common ancestor), than to group brown algae with some non-phototrophic stramenopiles (which share a common ancestor for most of the nuclear DNA), with which they share only inherited characters that need an electron microscope for detection.