Little suggestion (if possible) there should be some kind of indication for quotes which are already converted to invoices because it is hard to find in the list of quotes which of them are still pending to be converted
You might add custom field to sales quotes to track which ones are still open and which quotes are closed. You will still need to mark the quote as closed after converting it to sales invoice.
Status of quotes and orders is on the list of things to do. The developer is not going to be introducing this for a while as there are a number of items on the roadmap to be completed first.
A work around (not ideal) is to go to settings, custom fields and create a custom field (column) and put in things like open, closed, successful, lost business - each on a separate line.
Then for each quote, when you want to close it, you can select which field you want. Then when you want to view only open quotes - you can type open in the search field and this will show only open quotes (assuming that you have set each quote as open when you created it).
Not a perfect solution, but is workable until status quotes are implemented.