As a user I would like to see only the count of non-finished items in the left hand count so that I can easily see how many tasks are in the pipeline.
What would be great, especially with tasks, would be to remove the item from the count number displayed if the status was “X”, such as done. That way I could keep the finished tasks for historical purposes but would only see the number of open items. So if I had 7 items, but 4 of those were complete the number reflected would be 3 and not 7.
Hello @jharbour, welcome to the community! And thank you for your suggestion.
Unfortunately, I am not sure if something like this would be possible in Infinity. As you may know, Infinity allows you to organize pretty much any type of data - not only tasks. You can organize employees, ideas, leads, projects, etc. So it wouldn’t always make sense to have the number on the folder reflect a certain attribute - this number is supposed to show you how many items you have in each folder in general.
However, there are several workarounds to achieve something similar to what you need.
For example - you can create a separate Completed or Archive folder where you would drag and drop the completed tasks for a certain period - let’s say December Archive. This is, for example, how I organize my data in the Customer Success board. 
That way, you will always have your Tasks folder and the number will reflect the actual number of tasks which still need to get done. And you would have a separate folder with the number of completed tasks for December, for example.
Another way to separate tasks which are not completed from those that are done is by creating a checkbox for ‘Done’ or ‘Completed’ and then you can simply group your tasks by that checkbox, like in my image below.
As you can see, each column shows you the exact number of tasks which are done and which are not done.
To take this one step further you can also filter out to see only the tasks which are not completed - using the Filter option and filtering when ‘Completed’ is not checked.
Hope my ideas can help a bit.