I'm not sure "quantum leaps" were ever seriously described as "instantaneous". Headlines like OP haven't done much service to the more concrete (albeit layman) definition; when we are talking about quantum speed limits and propagation, what we are really getting at is the speed at which information is propagated through spacetime.
When we talk about the cosmic speed limit and why nothing can travel faster than light, that's what we are really trying to describe. Not that nothing can travel faster than light, but rather information propagates at a certain speed, which also just so happens to be the speed of light. The consequence is of course that nothing can travel faster than the speed of information propagation, not even "quantum leaps".
When we talk about the cosmic speed limit and why nothing can travel faster than light, that's what we are really trying to describe. Not that nothing can travel faster than light, but rather information propagates at a certain speed, which also just so happens to be the speed of light. The consequence is of course that nothing can travel faster than the speed of information propagation, not even "quantum leaps".