If deisgning a processor becomes profitable they will do it. It may very well happen in the future but for now the market needs are not so diverse that each has to have his/her own chip. The want microprocessors that run fast and consume less power if somebody does it for them then they are all the better because they can bargain too!
I feel innovation will suffer, if you leave it all to some few semiconductor vendors alone and commoditize the market. Anyway If you have the kind of volumes that Apple and Samsung have, then it should be certainly worth it to keep the design inhouse. When Apple released A5, it had the highest GPU performance compared to all other industry equivalents, eventhough everyone else had access to the same imagination GPU that Apple used.
Many of the customers I worked with did their own semiconductor design. Not just the processor, but also the power management and other components. I think this model has become less common in the industry due to the cost of new designs at cutting edge processes. The other model that worked very well for our customers was to have a parnership with semicondctor company to design a custom chip for them. They would have several of these "partnerships" and would end up using the chip that met their needs the best. This meant that the semiconductor companies were competing while designing a custom device. If you didn't win, you wasted a lot of resources.
Good point Frank. So many of the chips being used today are classified as SoCs, I try to refrain from that general classification. In addition, there is often more reason for custom designs of processor companion chips for RF and I/O because vendors may have very specific requirements or even proprietary standards like Sony. However, as more is integrated into the host logic or "processor" the same issues arise. Ultimately, the processor is the technology magnet for a platform, with the possible exception of analog circuitry.
Perhaps the question should be rephrased as "should OEMs design their own SoCs?" and should be asked with less emphasis on the actual processor(s) used in those SoCs. The number of companies that answer yes will be more than just Apple & Samsung.
Also consider that the SoC that contains the main host processor cores is not the only one in the system. The mixed-signal audio CODEC, for example, has evolved into an SoC of its own, and here again Apple is a standout. The CL chips that Apple uses today for this function are clearly customized just for Apple, so this "captive vendor" model is yet another option for large OEMs -- somewhere in between designing their own SoC and just buying standard parts.