Without deadlines there would be no pressure to get a project finished. Projects without deadlines can continue forever, as people continuously add features and try perfect the product.
More seriously, work tends to fill up all available time. So, if there is no deadline - or a very generous deadline, all the available time will be used up; and the project will still have trouble getting to a finished state.
On the other hand, deadlines create pressure.
- Some people don't work well under pressure, and their work would be better if there was no deadline, or a very far-off deadline.
- Deadlines cause people to take shortcuts, in order to meet the deadline. This could be a a pity, if the deadline is fictitious; it simply means that the project will need a follow-up project to clean up from the mess caused by the deadline.
This concept of projects without a deadline will have the side affect of dividing the team in 2:
- Those who continue to work fast, and always have their part of the project ready as expected. When they miss a self-imposed deadline, they will try catch up the lost time, or apologize.
- Those who take advantage of the freedom, and see no reason to speed up.