I still believe to let that icon either change from original cast to re-cast version ... or add recast to pop-up bar would be thousand times better.

Potentially, having recast pop-up appear in the say it won't take hotbar space could be desirable (honestly I doubt it will become a problem, but we will see as we continue using it).
I would be against casting changing into re-casting, because:
1) there might be situations where we do want to cast the spell on new target (for example switching target of a witchbolt)
2) If we cast a spell, we will probably want to recast it as well. Not an issue with spells one uses often that will be on the hotbar already, but as we gain levels, I suspect more and move players will be using spell level tabs to access spells they don't use in every encounter. As it is, they will be able to easily recast spells after an initiate cast, without having to dig for the spell again.