The purpose and value for daily pick of tasks

Uncertain what you mean by daily task picking.

The Development Team self-organizes around sprint work.   Per the Scrum Guide:

"Every day, the Development Team should understand how it intends to work together as a self-organizing team to accomplish the Sprint Goal and create the anticipated Increment by the end of the Sprint."

After task breakup the team starts working on them, usually ideal tasks are 1 day long, so in that case every member would pick a new everyday, is that what you meant by Daily task picking ?

So significance of this is that your user stories will complete and you might have a successful sprint :-)

It depends on the granularity of the stories itself. I thought those are meant more as tasks within the scope of a user story than being as a 'story'?

Daily task picking done by the developers themselves every day after they have done their task the previous day promotes the developer's commitment to the task. It makes them be able to focus more since the task they picked are surely the task they are more comfortable with and confident to finish by the next day before the next daily scrum.

I think that is the purpose and value of daily task picking for each day.