Yes you can make the distinction, and no it doesn't require getting rid of the microcode: https://news.ycombinator.com/item?id=37731829
Simply put, if the microcode can be updated by the user or remotely by Intel, then it count as "software", and Intel should stop shipping it. But if those update are either impossible or require a factory recall, then it's "hardware", and Intel can happily continue to ship it.
The same logic applies to the USB cable, and even FPGA: if the bitstream is locked into the NVCM, that's hardware. If it's merely written in the rewritable SPI flash, that's software. It's not a property of the bitstream itself, it's a property of how it is stored.
Obviously the cost of micro-code bugs will sharply increase. That's kind of a feature though: now hardware vendors must be really careful.
The problem is that you cannot make a hard distinction between hardware and software. An Intel CPU simply isn't going to run without microcode, and having to get rid of microcode would easily set back chip design by a decade.
Even something as trivial as a USB cable isn't pure hardware anymore. It has a programmable eMarker in order to advertise its capabilities, so it is also a combination of hardware and software. Everything but completely trivial chips has some kind of computation embedded in it, requiring some firmware.
Chips are complicated and weird. Pretty much nobody writes code which directly interacts with hardware. Even people who write code for embedded microprocessors will use an SDK provided by the chip manufacturer to smooth out the nastiest details. How's that supposed to work when the hardware vendor can no longer provide any software?
And then there's the question of what exactly constitutes "firmware". Is code in a separate programmable flash chip okay if they hardwire the Write Protect pin? What if the exact same code is stored in programmable space in the MCU itself? Is it fine to place that code in One-Time-Programmable memory? Bake it into the chip during wafer manufacturing? If anything, being able to update the firmware in the field is better for the consumer when it comes to fixing bugs.