After reading the question and answer that Joel Bosveld linked to in his comment, I installed Git to do version control of the novel I was writing.
If find the idea of version control intriguing, because I often rewrite parts of my fiction only to realize that a previous version contained some great phrases that I'd like to reuse but can not remember and have lost by rewriting.
The problem for me with Git is that I don't use it. I find the GUI unattractive, finding the relevant sections cumbersome, and the process of creating versions cumbersome. I have installed Git, "commited" (as it is called) the first version, and then never used it again.
Probably Git is intuitive and attractive for software developers who are used to that kind of tool. I grew up writing with a pen on paper. I am a visual artist. I want a "natural" GUI and interface. I simply find that I don't use a text editor like Vi(m) or a tool like Git, no matter how "powerful" they might be. I cannot warm for them.
So for me the answer is not that Git is overkill, but rather that it is too technical and abstract. It is not a tool make by and for a sensual person like myself, who loves the feel of paper and the sound of a pencil sharpener.
What I need is a writing software that automatically creates a verson whenever I save. The text editor TextWrangler (which I use for coding and for writing everything that is not a novel) does this. Every time you save, it automatically creates a copy of the current document in a backup folder of your choosing. The files all bear the same name (making them easy to identify), with a timestamp attached to it (helping you find a document from a certain period). Whenever I want to find some deleted phrase, I type what I remember of it into "Spotlight", the Mac file system search engine, which indexed the content of files as well as their names. All I have to do is delete the oldest files every now and then, but text files don't use much space, so these can go back years.
The only drawback with TextWrangler is that it cannot do markup: no italics, no bold text, no different fonts or font sizes. This works well for drafting of shorter texts such as letters, blog posts, StackExchange answers (lol) and so on, but not for text that needs such markup, like a novel or short story. I do often write out complicated paragraphs in TextWrangler and copy them to Scrivener once I'm happy with them.
This may not properly answer your question, but it will give you an idea. Look at screenshots of Git, read the documentation, and see if that is the kind of process that you find yourself attracted to. If you think it all looks quite complicated and not at all like writing, then you might want to avoid wasting time with it.