I do understand where you're coming from.
The reason I like the rage mode isn't because I'm a Bowser main, but it's the same reason I like random crits in TF2, it adds a wildcard aspect into the game that isn't able to be micromanaged and controlled by a human. It adds that "anything can happen" atmosphere to it, which makes it fun and exciting to me.
What it sounds like is that Jigglypuff and Falco have serious flaws that need to be addressed, not to remove rage mode. I completely understand where you're coming from, but you have to also understand the solution of removing rage is like tying your opponents arm behind their back to even the playing field. You also have to understand as much as Jigglypuff has an uphill battle, so do the heavy weights (you yourself even said you don't like them.) Watch this video and tell me Bowser needs another viable asset taken away. Just like you get killed as Jiggly super early and feel like you're trying to dig yourself out, Bowser gets comboed and juggled to like 70% from one grab. We all have issues.
You gotta make the bad aspects of a character better through patches and constant tweaking, not take away an opponents strengths. This isn't a "you think you're main has problems!? how about _____!" or anything like that and I DO understand why you have an issue with rage mode. Nintendo needs to tweak and balance those characters (including Bowser.) Make Falco and Jigglypuff have a few reliable KO moves.