Padding the Corner

Had a similar problem that we solved with a blob of Sugru. That rag looks like it would work about as well! Question is, why do we insist on putting sharp corners in places where we can walk into them? Seems like we ought to know better by now. I mean, how long have we been building our own dwellings?

This story still presents the endless conundrum between avoiding hurt and letting people learn and gain skills.
Assuming the world was mostly the same as nowadays, by the time your children are parenting, would they have the skills to notice sharp corners if they never experienced them ? 

I think my intuitive approach here would be to put some not too soft padding (which is effectively close to what you did, it's still an unpleasant experience hitting against that even with the cloth). 

What's missing is how to teach against existential risks. There's an extent to which actually bleeding profusely from a sharp corner can help learn walking carefully, anticipating dangers, and that these skills do generalize to many situations and allows one to live a long fruitful life. (This last sentence does not pertain to the actual age of your children and doesn't address ideal ages at which you can actually learn the correct and generalizable thing). If you have control on the future, remove all the sharp edges forever. 
If you don't, you remove the hard edges when they're young, instore them again when they can/should learn to recognize what typically are hard edges and must be accounted for.