Is ROS the right approach for building a robot controller from scratch?

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I'd tend to agree with @Alex-SSoM: if you don't have experience with this sort of thing, or the drive to gain that experience, it's going to be a difficult process. Unfortunately there isn't really a "ROS package for retrofitting old industrial robots/controllers".

However, if you like reverse engineering things, and have access or can acquire the necessary parts, it can be done.

To make this a little more than a one-line answer, two recent examples:

Tormach ZA6

Link: Tormach ZA6.

An (older) presentation about it from the ROS-Industrial youtube channel: Tormach - A ROS-Based Open Industrial Manipulator. And a blog post by the OEM themselves: ROS Makes the Difference - A Tormach ZA6 Robot Customer Story.

Tormach had years of experience with their CnC machines, and years of experience with OSS control software. Adding ROS was just an extension at that point (but it's certainly still an achievement).

Pilz PRBT

Another example would be the Pilz PRBT (and on the Pilz website). Discontinued now, but in essence also a "ROS-based robot" (ros_control, ros_canopen, MoveIt, IKFast, etc). Many of the packages are still available, so you could take a look at how they approached things.

Of course, Pilz also had decades of experience in motion control when they started this development, and some talented developers and engineers (some even became MoveIt maintainers for some time).

Edit:

So I am thinking about the possibilities to revive this little guy by getting some AC servo drivers for powering the motors and, from a bird’s eye view, use a computer for doing the controlling tasks

If you can get servo controllers to work with the robot's servos, that would be the biggest problem solved.

The software part after that is doable in most cases.

While everything is possible, I would advise you to find the original kuka controller for your robot. If you were to build a complete new controller from scratch there's quite a bit of stuff you'll have to reverse engineer. Also, most robotic arms have some sort of embedded and/or real-time motion execution controller. ROS is usually used to send high level commands to the internal execution controller of the robot.