This picture shows the fingerprint reader is within the PCB
So for the FP3, it would make the device a bit more bloated (thicker). Although, yes, perhaps you could replace the physical part of the fingerprint sensor with something else without bloating or changing case.
For a FP4, the thing is, people (reviewers) in general do not like a fingerprint sensor in the back. They prefer it on the front (when bezels were still larger), behind the screen (because bezel size has diminished), or on the power button (because bezel size has diminished). A FP4 would follow the trend of solution #2 and #3. That, or something akin to FaceID (solution #4).