The two key arguments in the paper are: 1) Cell membrane invagination isn't sufficient to overcome the energy well of prokaryotic cells; 2) Endosymbiosis is the only mechanism to provide the energy necessary to give cells a chance at complexity.
http://www.nature.com/nature/journal/v467/n7318/full/nature0...

In re: 1,

"Mitochondria must respond quickly to changes in membrane potential and the penalty for any failure to do so is serious. The electron and proton transfers of chemiosmotic energy coupling generate a transmembrane potential of 150–200 mV over the membrane (~5 nm across), giving a field strength of about 30 million volt per metre, equal to that discharged by a bolt of lightning. This high membrane potential sets the inner membrane of bioenergetic organelles (mitochondria and chloroplasts) apart from all other eukaryotic membrane systems. Failure to maintain the mitochondrial membrane potential is penalized by a collapse in energy charge, blocking active transport across the cell membrane, and a rise in free-radical leak, which in eukaryotes and many prokaryotes leads directly to programmed cell death.

....

"This requirement for physical association of genes with bioenergetic membranes to maintain ATP synthesis constrains both the genomes and the complexity of prokaryotes. If some genes for oxidative phosphorylation must be physically associated with a certain unit area of bioenergetic membranes, then beyond that threshold prokaryotes could not maintain membrane potential homeostasis unless additional genomes are co-localized with the membranes."

In re: 2,

"The main difference between endosymbiosis and polyploidy relates to the size and distribution of genomes over evolutionary time. In endosymbiosis, surplus organelle genes are lost or transferred to the host’s chromosomes, streamlining endosymbiont replication via cytoplasmic inheritance. The outcome is a massive reduction in genome size, both in prokaryotic endosymbionts and organelles, with a reciprocal relocation of genes in low copy number to nuclear chromosomes in the latter. By contrast, in giant polyploid prokaryotes, all genomes are essentially the same. Without cytoplasmic inheritance, no genomic specialization ensues.

"In principle, prokaryotes could control respiration using specialized, membrane-associated plasmids that emulate organelle genomes in gene content and function. In practice, such plasmids are not found. Bacteria usually have small, high-copy-number plasmids that segregate randomly at cell division, or very few giant plasmids that co-segregate with chromosomes on filaments from midpoint. For plasmids in a prokaryote to support electron flux as organelle genomes do, high-copy-number giant plasmids encoding components of the electron-transport chain would need to associate with the plasma membrane, and evolve counter to the tendency to segregate with size rather than function. That no mtDNA-like plasmids are known indicates that high energetic barriers preclude their evolution: unlike organelles, which pay back energetically from the start, substantial energetic costs must be paid up front (high copy number of the correct plasmids, and the machinery to associate them with the membrane at regular intervals) before any energetic advantage can accrue.

....

"Thus, being large and having masses of DNA is not enough to attain complexity: cells need to control energy coupling across a wide area of membranes using small, high copy, bioenergetically specialized genomes like mtDNA. Segregating the genes relinquished by the endosymbiont (mtDNA) into low copy number in the host’s chromosomes, specialization of the endosymbiont into an ATP-generating organelle and increasing organelle copy number provides sufficient energy per gene to support the evolution, maintenance and expression of some 10^5 more host genes, affording the cell the chance—but not the necessity—of becoming complex."