Being able to open them as well would be nice, but allowing users (of at least TL2, if not lower) to close their own topics would help in a lot of cases and prevent what is described in the thread below from being an issue.
https://meta.discourse.org/t/adding-additional-flag-options/108057?u=orangeandblack5
I also know that other forum platforms do allow this, so it would be nice to be able to open and close our own topics if we need to.
Flagging is the correct course of action here. I suggest if you need users to close their own topics you should promote them to TL4.
But this will potentially harm the Trust Level of the topic creator, right?
This seems like a bad side effect…
For these you’d need to use a ‘something else’ flag to ask the question, and those don’t affect the trust levels. 
(only agreed flags of ‘spam’ or ‘inappropriate’ count, and that’s only towards the TL3 requirements rather than being part of all trust levels)