Jack Kruse sent me this link:
Archaea with eukaryotic genes
For those working through Nick Lanes latest book will realise (if you hadn't already!) that there is an energetic cost to everything. The ability to change shape at will, with a view to phagocytosis, is both an essential to the development of the eukaryotes and is energetically very costly.
In the absence of mitochondria the only place this appears to have been discovered is the deep sea alkaline hydrothermal vents, in this case at Loki's Castle. This is the environment where geothermal sources generate the electrochemical disequilibrium which probably got life started using the "free lunch" of CO2/CO plus R-SH giving acetyl-S-R, gateway to metabolism. It is still an energy rich environment.
Phagocytosis is costly.
The alpha proteobacterial precursor of our mitochondria had to get inside the archaeal host. This is an interesting discovery relating to how that might have happened. The phenomenon of archea performing ingestion may well have remained confined to the vents if it was too energetically costly in the open ocean. Unless that archaea was carrying little mitochondrial powerhouses, in which case it was pretty well already eukaryotic. Far from equilibrium environments make for interesting developments.
Looks like you can develop eating only if you already have a free lunch!