Thickness is likely a factor if Apple wants to use the same FaceID module across multiple product lines. However, decent chance also that having two FaceID cameras is a limited factor also. Phone SoC chips typically have special bus for linking the camera module to the image processor+camera controller inside the SoC. Probably the case there isn't more than 3 connectors there ( and some sharing of a bus for a fourth camera).
For example, the Snapdragon Elite 8 (Samsung Fold 7) in the camera specs ( have to expand the tech spec view)
"...
Image Signal Processor (ISP) Number: Triple ISP
Image Signal Processor (ISP) Bit Depth: 18-bit
Triple Camera (MFNR, ZSL, 30 fps): 48+48+48 MP
..."
The Snapdragon 8 Elite Mobile Platform is performance transformed.
www.qualcomm.com
pretty good chance there is only three camera inputs on that SoC and there is kind of camera 'switch' IC inside the system to flip between on one of those paths. There is no FaceID depth sensor array in that set-up.
FaceID requires more than normal camera bus width. There is more than just visible image data coming back from the expanded sensor array. So decent chance there is only one "FaceID" expanded data bus on a normal Apple Silicon chip.
In that case, Apple designing/making an 'even thinner' FaceID sensor array wouldn't solve the problem anyway. It is also likely too early to throw a feature that won't be used at 100's of millions other Apple devices. ( 'Fold' will share A-series with other Apple products that sell in orders of more magnitude more units. )
A workaround would be to have FaceID only on the outer 'selfie' camera, but that would be quirky when in the open mode and want to do things like authorize Apple Pay. At root is the disconnect is the usage as a 'full phone' when closed and also when open requiring two instances of the authentication mechanism. Going to a TouchID sensor means only have one authentication module for both modes. It is more simple.
The 'thinner' half isn't going to help the TouchID sensor if they make it too small. So it isn't a 'free lunch' going in that direction.