Ignoring broken windows is a bad idea -- it's important that the community see
there is a system of rules here that are enforced; if you ask poorly, your question may be closed too
the closed questions, if closed incorrectly, can be peer reviewed, edited for improvements, flagged, or (assuming enough rep) voted to open.
Both of these things are critically important and neither can happen if we hide the "dirty laundry".
Now, if more than 50% of the questions on the home page are closed, then the site has much deeper problems of scope topic and messaging -- but you have provided no evidence that this is the case.
495 closed questions
so about 8% of questions are closed; statistically this means on a homepage of 48 questions you can expect to see 3 or 4 closed questions. But this is necessary and even good for reasons #1 and #2 above.