The implicit assumption with decompiling code is that the goal is either to inspect how the code works, or to try compiling for a different machine. I’ll try to explain why the latter is quite difficult.

As you said, compilation to machine code only keeps the details needed for the CPU to accomplish what was instructed. And indeed, that is supposed to be efficient to run on that CPU, by reason of being targeted exactly for that CPU. But when decompiling, the resulting code will reflect the specificity to that same CPU. If you then try to compile that code for a different CPU, it will likely work, but will likely be inefficient because the second CPU’s unique advantages won’t be leveraged.

To use an example, consider how someone might divide two large numbers. Person A learned long division in school, and so takes each number and breaks it down into a series of smaller multiplications and subtractions. Person B learned to do division using a calculator, which just involves entering the two numbers and requesting that they be divided.

Trying to do division by blindly giving Person B that series of multiplications and subtractions to do on the calculator is extremely inefficient because Person B knows how to do division easily. But Person B is following Person A’s methods, without knowing that the whole point of this exercise is to just divide the two original numbers. Compilation loses context and intent, which cannot be recovered from decompilation, for non-trivial programs.

Here is an example why source code is useful when it provides context: https://en.m.wikipedia.org/wiki/Fast_inverse_square_root#Overview_of_the_code . Very few people would be able to figure out how this works from just the machine code.