Choosing tools and technology can be a formal process that locks you into your choices, or a chaotic process where nobody knows what the choices are.
The correct way to document a decision is to supply just enough information to explain why the choice was made at this point in time, what alternatives were considered, and what exit plan you have if the choice doesn’t work out as well as you hoped.
As soon as the process is to “justify a choice” in order to gain approval, it has gone too formal.
You see, this kind of decision making suffers from amplification. If you make choices easily, you can change them easily. But if you need a signature from a corner office, you’ll get stuck in a loop that goes like this… if your boss signs it and you decide to change your mind, you’ll need to “admit you made a mistake”… which makes your boss trust your decision less… or maybe you just won’t change your mind… and if you think too much about this in the first place you’ll take longer to make any decision at all.
So maybe you should keep your decision making lightweight.