Story X is committed to the Sprint. Developer A has 8 hours capacity per day. There are no other Stories (for the sake of this example). She says that the Story X should be enough work for her for the day.
However, Developer A has created a task for the day called "Investigate issue and determine next steps = 4 hours". She believes that after completing the 4 hour task she will have more info to complete the rest of Story X for the day. She'll create tasks then.
At the beginning of the scrum only 4 hours is committed by this resource.
Is this OK?
Can she not create assumptions and other tasks in rough estimate? e.g. SURELY there are development tasks and unit test tasks after the 4 hour analysis?
I am hesitant to let a team member start the day off with only 4 hours committed.
The situation you describe would be OK if it represented a team consensus on what was plannable. However, you seem to be describing a situation where one developer alone has attempted to plan tasks for a story. That would not be acceptable.
The planning of tasks, whether it be done in Sprint Planning or following a daily Scrum, must be a joint team activity.
I suspect that if this happened, the team might well be able to plan enough for the day ahead, even if only in "rough estimate" as you suggest.