Near the later phases a hole appears that the player can enter and it's implied that enderman made the hole but there's no proof this is what happens

So to make the illusion that they are pulling the blocks off of the wither storms enderman can spawn near the wither storm holding flesh blocks

I love this idea. I really hope it gets added in a minor update, or at the very least in Evolution pt. 2

This is a great idea! If new endermen get spawned, then i have an ender pearl farm idea.

You need ender pearls to get into the wither storm anyways so this would be very helpful.

This could actually be useful beyond immersion.
If Endermen can keep spawning with random Wither Storm blocks after it's been defeated, then that makes them renewable without having to keep the storm alive to gather as many as you need.
Or maybe there are plans to involve the withered star in creating more of these blocks?