[FiatLuxDave]

Yes, dunking bird style evaporation engines are among the lowest efficiency kinds of evaporation engine. One of the big reasons for this is that the process is using evaporation to create a temperature difference where the cold is generated at the same place the evaporation occurs. Evaporation works better when it is hot. This is a negative feedback which reduces the effectiveness of the system.

Fresh water is not a strict requirement for most evaporation engines. It is the low efficiency which drives that. In theory, the osmotic energy difference between fresh water and sea water is much smaller than the energy obtainable from the evaporation process. After all, seawater is observed to evaporate! However, when your efficiency is under 1%, even a low additional cost becomes a big one.

IIRC, Carlson, from ref 1 in the energy tower article (I remember adding that reference to Wikipedia in 2006!) had a design which used a Stirling engine running off an evaporation generated temperature difference which had the same negative feedback problem. There are other designs, like the piston-based one which Barton worked on before pivoting to a co-generation system (Hmm, that seems to have fallen down the Wikipedia memory hole - https://handwiki.org/wiki/Physics:Barton_evaporation_engine ).

Efficiency is always the big challenge for evaporation engines, but the strict thermodynamic limits are much higher than any current design. This means that there is a lot of room to improve! One of these days I'll write a paper on that.