Character growth and development is what defines the broad net. It's the "RGP Element" that so many developers have injected into other genres. Where JRPG and WRPG differ is largely in how the player explores the role of "character".
But if that is the case, how do you explain games like Final Fantasy VII and VIII, where the growth of the characters themselves is almost immaterial, and the system is centered around developing their equip-able items? Things start to get murky when you expand the definition to encompass such a broad swath. I really think what we need is another term, one that better describes the sub-genre, instead of just expanding the scope of "RPG" to pull double duty. Perhaps "ASG", for Adventure Statistics Game.
I don't care how kawaii uguu~ desu a game is, even if it has a completely static story and terrible characters, it is still be an RPG. If you want to go around saying that Final Fantasy 7 isn't an RPG because Cloud is about as interesting as a cardboard box (which I completely agree with), you can, but I don't think many people are going to agree with your genre classification.
RPG in the video game sphere more or less means "Adventure Statistics Game", but people call it RPG because of the games they grew out of. I don't think people go around calling hack 'n slash D&D campaigns "Tabletop Adventure Statistic Games" just because the players aren't heavily role playing their characters. The defining characteristic of the genre is in fact, not its role playing, but the statistics growth and (numerical) character progression.