I wish to give every registered users to possibility to decide who the assigned person for the new task is. I don't want that only the administrator or super user can decide while creating a new task for whom it will be assigned too. Nor do I want that the super user to have to change the assigned person every time from inside the task. Making it by default that all the registered user can decided who they want from the creation page.
Thanks in advance to any possible solution.

That is not built in, but you have the full source code, so it is possible to do what you need (or pay someone to do it).

The reason that is not built in, is that is something that is easy to do for a specific situation (so it would not be too hard to have it changed the way you want), but is very hard to do to make "user configurable". Basically it is "Rules and Workflow".

So we totally avoided that for now because having a "Rules and Workflow" engine that doesn't work well or is confusing is a very bad thing