Yeah, that was the standard document control method 20 years ago everywhere. It works, but it's incredibly inefficient.
Such systems make any sort of global changes extremely taxing (so many people need to sign off on it, and there's going to be loads of bike shedding), and naturally favors heavy compartmentalization. The work winds up divvied up among many people working in parallel, but they're not collaborating - you're waiting on mike to finish his portion, not working with mike to make a better document.
It's also very difficult to efficiently divide labor - for example let's say you have an equation heavy document, you could have one person do the first half and another do the second, but it would make more sense for one person to do the text and another person to do the equations as that way neither of you have broken flow. This is possible but a real pain in the butt to do simultaneously with check-in check-out, alternatively you can have the one person do the text and then hand it off, but that might be very suboptimal if you are time constrained. This sort of work is a breeze in a modern collaborative environment though.
Finally, from a true document control perspective, the old check-out method seems sensible as you know what changes were made between when it was checked out and checked in, and you know who checked it out, however you don't really have any better knowledge than that. With a modern system you can see who typed what and you can see every edit they've made, including when they've typed out a long section then decided to delete it and try something else. This can be incredibly useful for keeping track of how an idea evolved. It's also easy to see who actually contributed what: while traditional document control will tell you that so and so made a change to some section, if the change was just pasted in it's difficult if not impossible to tell what the difference from the previous version was. Finally while traditional document control focuses on limiting the chances of a mistake, modern methods allow you to fix mistakes easily.
Now I'm not saying that there's no way to get what you need with check-in check-out document control, but we've reached the point where you don't need to make your work compatible with the process.