However, git lets you fix the mess in such a way that you'll have a clean commit history. This is really helpful if you're trying to keep your codebase clean so that `git bisect` will always work nicely, and if you just want to keep your codebase history really grokkable.
When I do personal development or small side projects I could care less about my history being clean. Nothing is ever so large or complex that it needs to be fixed in such a meticulous manner. It may feel that way, until you start working on larger software. The stress of a $1,000-$20,000 job is laughable compared to the scale of enterprise failure.
In enterprise, it's often the case that applications are built by teams of people in constant flux. They may need to be patched or rolled back at a moment's notice, and every hour the bug stays live is an hour of enormous financial burden to the client and intense stress on my employer. In this case, having a trustworthy VCS with a clean history in invaluable.