GNU assembler alternatives

ince I really like the idea of atomicity of each program in unix-like approach

I'm not one to tell you how to interpret some philosophy, but I think your assumption that an assembler without a linker would be useful for building software is wrong. Same for a compiler; these three need to work tightly together, and them belonging to one and the same software project makes a lot of sense.

Generally, the "UNIX philosophy", however you define that, definitely does not say "all programs are completely freestanding without shared code with each other". Completely the contrary must be the case – one of the cool thing about "original" UNIX was that it quickly supported virtual memory and linking against libraries. So, by no means are UNIX programs "atomic"! That's literally the opposite of what being able to use POSIX system calls like dlopen, or the idea of POSIX shared memory suggests (and that's been around since at least since SysV, around 1983, as far as a cursory search tells me.
So, maybe reduce your "desire for purity" there; UNIX itself isn't meant to give you atomic programs, but to allow you to compose programs out of pieces in function libraries, and make them work together on files exchanged through a stable file system.
That's why C exists – because Kernighan and Ritchie needed a language that allowed them to do exactly that, build programs that interact with components, and assembler did not provide a defined calling convention.
People confuse "no piece of code can have more than one purpose" with "compose complex scripts by piping output to standard input of the next process", but that concept is actually far less central than the idea that you can call functions from libraries that you could share with others¹.

That being said:

You can of course build and install the GNU assembler alone, but it won't be very useful. So, there's no problem here to solve; just ignore the things you don't want.

If you want to build a kernel, you will need to go with the GNU assembler or maybe the llvm-as competition (which is even more modular and pretty much useless without the clang C frontend).

^{¹ And frankly, I'm kind of annoyed by the claim that "every program has only a very singular purpose and that's a good system design for everything". I'm sure you prefer editing your text files in ed rather than vim or emacs, and I'm sure as a UNIX purist you hate awk with a passion, as it does allow you write complex text processing programs instead of composing them via endless concatenations of programs through file descriptors, and the idea that your shell can both be used to launch programs and count to 1000 is a travesty to you – but for me, programs having useful feature sets rather than minimal ones seems to make my day more productive. I'm not sure how one would reconcile "single-purpose tools are the optimum" with using a web browser, which explicitly is all – a news reader, a question&answer platform client, a mail client, a video player, a practically endless collection of games, a client to text chat networks, …}