Assembly Language – Why Convert Instead of Machine Code?

for the very first assembler ever written (i.e. in history), wouldn't it need to be written in machine code

Not necessarily. Of course the very first version v0.00 of the assembler must have been written in machine code, but it would not be sufficiently powerful to be called an assembler. It would not support even half the features of a "real" assembler, but it would be sufficient to write the next version of itself. Then you could re-write v0.00 in the subset of the assembly language, call it v0.01, use it to build the next feature set of your assembler v0.02, then use v0.02 to build v0.03, and so on, until you get to v1.00. As the result, only the first version will be in machine code; the first released version will be in the assembly language.

I have bootstrapped development of a template language compiler using this trick. My initial version was using printf statements, but the first version that I put to use in my company was using the very template processor that it was processing. The bootstrapping phase lasted less than four hours: as soon as my processor could produce barely useful output, I re-wrote it in its own language, compiled, and threw away the non-templated version.

I find this definition pretty clear:

The Instruction Set Architecture (ISA) is the part of the processor that is visible to the programmer or compiler writer. The ISA serves as the boundary between software and hardware.

The ISA provides an abstraction of the actual microarchitecture, which is the implementation of the instruction set by the processor.

So when your compiler is said to produce machine code, it produces instructions for the configured instruction set, not the actual processor, so any processor implementing that instruction set can run that machine code.

A virtual machine such as the JVM or CLR runs code that has been compiled to bytecode specific to that virtual machine's architecture, Java bytecode and CIL in this case.

The runtime of such a virtual machine, which in turn is built for and runs on a specific processor architecture and OS, translates the bytecode to the machine code and API calls for the platform it runs on, and usually does so just-in-time.