Why are there no motherboards that are designed for both Intel and AMD CPU chips?

Because the use fundamentally different bus architectures; see HyperTransport and QuickPath Interconnect for the details. Physical similarities in the arrangement of pins, etc, are mostly down to the physical realities of building a CPU dictating much of the form.

At a larger scale, the answer is: because they believe they have more to gain from incompatibility, for business reasons, than they do from compatibility.

Universal replacement parts fit universally badly.

At one time when AMD was licensing from Intel to produce 386 and 486 chips, it was possible, but with the Pentium forward, this compatibility disappeared with divergence between the Pentium and the AMD line. This led to the necessity of having different support chip sets and therefore different motherboards.

MBs can't be designed for both Intel and AMD CPUs because they don't connect the same. There's far too much different going on in the connectors to make it easy to do so. They don't operate under a standard bus design. Similarly, different generations of Intel/AMD chips won't work with MB from an older generation. The electrical and protocol requirements are too different for it to work.