Indeed, a rota can be an inefficient method of tracking tasks and responsibilities. Especially when you print out a quick-n-dirty table from Word onto a piece of paper.
Of course you’ll run into problems! It’s for all of the reasons stated in the blog post that computers often take over the role described.
(And, obviously, you have created a wonderful application that solves of your presented problems! It’s effectively a computerized rota, no?)