I think it actually makes (financial) sense that they aren't using BSI on the A7S right now.
(I'm just linking to this article because they have a pixel pitch chart)
https://photographylife.com/sony-a7r-ii-use-considerations
The A7RII has a pixel pitch of 4.51 microns, or 20.34 square microns.
The A7S has a pixel pitch of 8.4 microns, that's 70.56 square microns.
If the amount of surface area occupied by circuitry is the same per pixel, just for a harsh estimate lets say 10 square microns, then the A7S would be losing approximately 14% surface area per pixel... But the A7RII would lose 50%.
Using an expensive fabrication method to get back 14% of your sensor's potential doesn't sound that appealing.
Sony probably loves that the A7S is so popular, the margins on a sensor with pixels that large are probably a lot higher just based on the lack of complexity.
I have a theory that IBIS is the reason the A7SII is worse than the original though.
The A7II (not the S or the R, the regular 24MP model) also had worse low light performance than the original A7, and the only reason I can think of for that to be the case is the In Body Image Stabilization, probably just because of thermal dissipation.
One thing I notice when shooting Macro with long exposures is that I get way more hot pixels when I'm using live view, I hate to say it but I actually prefer not to use live view if I really want a clean shot.
I assume that most cameras are designed with a good thermal management solution, but IBIS demands that the sensor be floating, you probably can't have a big heat sink stuck to the back of it at the same time. Thus, noisy pixels at high ISO.
Or so goes the idea in my head anyway.
How does the A7RII get away with it? Who knows. Maybe Backside Illumination also lets it offload heat better because the circuits are on the back? And maybe it also insulates the photon wells from heat generated by the circuits? This would indicate that BSI on the A7SII would be a good idea, but, margins. Just like Canon and their old sensor fabs, if you think the improvements are minor and you can sneak out old tech for a while longer, that's going to be extremely enticing.
What I know for sure is that I like high resolution cameras and I'm very glad that BSI is working so well on the A7RII.