This type of numbering system makes all keys universal. With this approach you can play any song in any key that you know the scale of and the chords for. For songs that change keys, just choose the major scale that fits the best.
I've created a table containing boxes representing measures/bars to use as a template for writing out songs this way. For songs where the melody comes straight from the vocal melody, I also write down the lyrics and apply a note number to each sung syllable.
Here's an example lead sheet for the song I Wonder Who's Kissing Her Now. I encourage others to try this. It's also good ear training because it's less visual and less tied to a certain key or fingering. It makes it easier to practice a song in all 12 keys and in various ways, which is good for building an aural connection.