This feature would indeed be very useful!

The side bar in Day view should be able to show tasks in the following order:

1. Tasks on or past their due date (like today)
2. Tasks on or past their start date
3. Undated tasks, sorted by user priority (see separate idea 'Task sorting by user priority')

example 1: you want to charge your car battery every autumn, add a repetive task with a start date of october 1st (no due date). It should then appear in your task list on october 1st as todo and when checked, it disapears.

example 2: you have kids (not that old) and they mention sporadic what they want, then add a task, start-date December 1st, due-date dec 20th, and all the sporadic ideas as description. then it will popup in your todo on december 1st, remembering you what to buy

example 3: cut trees/hedges around the house, create a repetive task start date feb 1st, due date feb 28th. it will display in yout todo list feb 1st and go away when either, checked or due date is up.

the task widget could have an additional option "Visability of not started tasks" to either display only started tasks (display all tasks without start date, and the ones with passed start date), or all tasks. Integrating into "Visibility of passed tasks" is also ok, this will allow for a smaller todo-task widget up front and a larger on a less used page.

please I really miss this feature...

Sometimes there are tasks they have to be done during a period (e.g. two weeks) until an end date. It would be better then to show the task every day in this period until it gets marked as done.