What if you dribble...and don't pick it back up for, say 4 or 5 steps. That gets called, but by the definition you are giving, it shouldn't. Or if you don't gather it, but just let it slide around on your hand, or body, for a few steps? That's not legal either, but would be by your definition above. They are making this a whole lot more complicated than it needs to be. Leave it to the NBA to make the simple complicated, and then wonder why people castigate the refs so much. Like the NFL with their f'd up rules on what a 'catch' is.
This is legal. The dribble does not end until you hold it, or control the ball enough for it to come to rest, to pass or shoot, or it becomes dead while in your control. No where does it say that you have to dribble every so many steps. Manu dribbles through legs of defender and he catches up to it No call. The most common example is PGs will dribble in backcourt with no defenders and wipe their hands/shoes while letting the ball dribble as they are walking. You're right. They are not legal and they are not part of the definition of travel, either. It's not in the definition of travel wrt gather, because these things are not Traveling Violations. One is a Carry Violation (getting hand beneath the ball), and the other is Double Dribble (touching the ball twice with either a hand or other body part before you dribble again). I'm here all night ... AMA!
Sounds like you have a problem with the 2-step rule. This is a quote from article I posted on the previous page. Joe Borgia (Sr. Vice President of Replay & Referee Operations) says he has done this same exercise watching classic NBA basketball players like Pete Maravich, and he's wholly satisfied that there's nothing new about allowing two steps. "The normal, basic layup, eighty percent of the time the player is going to gather the ball with a foot on the floor, and then we give them a one, two."