I think it's not as type-related as people make it out to be. I know an INFJ (family friend) who procrastinates to the last possible minute - it irritated his mom for years up until this year when he left for college. His older ISTJ brother on the other hand finishes everything like days or weeks in advance. The only types I've known to be organized by nature are EJ types. And even then I know some of those type who procrastinate - I think it's just that they're more aware of how they could be using their time efficiently so it bothers them more.
Ps are probably known for putting things off more because we like going with the flow and moving without answering to a schedule. And P types probably do procrastinate more than Js on average.
This is a good point, I think I would say I am one of those procrastinating EJ types. I think it can often have something to do with the development of the secondary function and I tend to subscribe to Lenore Thompson's view of it.
The suggestion being that a person has to consciously engage with the world in a way that develops that second function and more importantly; learn how to train it on either perception or judgement of themselves. This grants a stability and introspection to a person.
However I think it's important to note the difference with regards to the procrastination of, let's say, an ENFP and an ESFJ.
Fi in an ENFP will help them examine what they really value and how they stand amongst that value, along with picking out the Ne notions more in line with meeting those values. However this probably won't stop procrastination which, as you pointed out, is more natural to P types, in this case Ne is a big factor in that natural.
With ESFJs Si brings the structure and security of the familiar and comfortable, allowing them to better organise themselves and makes their judgement more discerning and less arbitrary. It does of course depend on what those sensory impressions were, but generally speaking they induce a drive to pull structure into an environment by bringing things in line with those impressions.
Fe > Ne without that structure is a flighty nightmare of jumping from group to group for attention and changing moods, which is also lacking a grounding element towards some form of reality.
This can result in an ESFJ looking superficially like an ExFP type at first glance.