A question that has no answer is easier to fix (make on topic, narrow the scope, fix the XY problem, remove polling nature) than one that has several answers.
A question that is closed quickly means that the author gets faster feedback on what is on topic and what is not on topic, preventing possibly a series of poor questions and a question ban.
A question that is a dup allows the asker to find their answer in a prompt manner or fix t the question so that it asks something that isn't a dup.
A question that is migrated quickly allows the asker to get an answer on the target site in a reasonable time. Prompt migrations means that questions don't get reposted on multiple sites when there is no answer on the first (because its being migrated).
Closed questions feed into the question ban system. When someone doesn't clean up their questions, closed questions will help the community by preventing someone from draining the resources of the community.
Closed questions can be automatically deleted by the 'roomba' - a series of scripts that will delete questions with low scores. (yes, there are criteria for non-closed questions too)
Closed questions can be deleted by 10k users. Those questions that are just embarrassingly bad but have some criteria that prevents the roomba from deleting it (upvoted answers, accepted answers). These can't be deleted until they are closed.
All too often, open questions are used as justification for asking another question in a similar vein. The Asker searches for something, finds an open question (that should be closed) similar and asks another question (that should be closed), and now there are two broken windows on the site rather than one. If the asker's question is then closed they see an inconsistency in how things are dealt with and this can result in a negative experience relating to Stack Overflow.
While it is not critical that things be closed, closing questions helps maintain the average quality on the site:
- Deleting poor questions
- Educating users about how to ask a question
- Keeping poor answers from answering poor questions