Does anyone think that the upcoming expiry of patents on the core x86-64 instruction set which includes SSE2, maybe sooner than 2023 (as the Athlon 64 was introduced in 2003) would open the flood gates for third party implementations of compatible processors?

The basic architecture including importantly the memory model could freely be implemented in hardware once that core instruction set falls out of patent; I'm unclear about the amount of traction that later Intel instructions have gotten in common software, but emulation could at least ensure compatibility. Competition in x86 implementation has languished for long stretches of time, though it has seen a resurgence as of late; compare that to the ARM ecosystem which has seen vast improvements due to a larger number of implementers: Apple, Qualcomm, nVidia, Samsung, ARM, Applied Micro and Cavium.