We are venturing on my opinions now but yes, the ASIC development is important in my opinion. It really is exercising the "pipeline" for computer programs baked directly into chips. It is the direction the industry is moving and why you see so much activity in the RISC-V space for example. This tech is the future for faster computing / more efficient computing. I am not actually sure though if tech like RISC-V is used today in the ASIC miners. I think I'll look into that.
Is the development of bitcoin ASICs actually driving any general purpose advances? My understanding is they were just applying existing advanced technology to Bitcoin. The idea of an ASIC isn't new, and Bitcoin mining is niche compared to other areas (e.g. cell phone processors, desktop CPUs & GPUs)