score:4
Most airlines have interactive route maps that do exactly what you're looking for.
In your very question you've called out the JetBlue route map tool claiming it doesn't do this - but it does. Simply select the "Non-stop" option, and then select an airport and it will show you only direct flights from that airport.
These generally will not show frequency, which isn't surprising given that frequency changes day-to-day and month-to-month. Once you know that a flight exists, simply searching on the same website for that flight on a specific day will show the number of flights available on that day.
Upvote:1
If a particular airport has a tabular listing of all flights, usually you can copy the entire table and paste it into a spreadsheet. Then you can filter or sort by any column easily.
This works on almost any HTML table in Safari. I think I've also done it with other browsers.
If you get unwanted formatting, you can paste special or first paste into a plain text file.