Correct it is only the air to glass surfaces that would be (are) coated, but the coating process involves a vacuum deposition (e.g. of MgF) or electron beam coating or whatever and many of these processes require the glass to be separated from its companions, for the rough grind, polish grind, vacuum, ... which are necessary, and then reassembled.
All this is ok with an early lens which uses the natural glue, the later lens use synthetic glue and the glass elements may not be as easily separable. There is more risk of physical damage.
It would be a gain to coat an uncoated sonnar, it would not help (as much) to multi coat a coated sonnar. The difference between the single coat and multi coat for 6 air to glass coatings (three group) for a deeply curved lens are minimal. The lens was designed to be uncoated...
The new 2000 S3 nikkor is a computer optimised design with best glass and coatings. It may need the modern coatings more, it is probably a four group, it may employ high refractive glass and therefore need better coating and may have several less deeply curved surfaces and therefore need better coating.
Noel