Well it's certainly much cheaper than designing a new CPU where all the parts have to be designed from scratch (or "upgraded" from previous design). E.g. going from Richland->Kaveri should be much more expensive compared to reusing IP blocks from the Kaveri design in a 6/8 core CPU based on the Kaveri Steamroller CPU core.
Regarding the reason why we're not seeing all the possible CPU versions you mentioned from AMD, I would say the primary reason is that AMD sells in much less volume. So they simply can't have that many SKUs, because the volume of each SKU would be too small. Entering a new segment would be a different matter though. I.e. if they make an 6 & 8 core CPU without iGPU, they can enter a completely different market segment for relatively little cost. Hence it makes sense.
Also, look at Intel instead and the multitude of SKUs they have. Surely they would not have so many SKU variants if it would require a huge additional cost for each SKU.
It's not just about whether or not the potential profit offsets the initial costs - AMD needs to have the money to make those different SKUs in the first place. Intel has a lot of volume potential and they also have a lot of money. It may also probably costs less for them to make all these different dies because they own the fabs.
But yes, if they can afford it in the first place then it comes down to volume.. and in the end FX may now basically be just another SKU they can't justify a die for.