Interesting thought - I also want to enable the auto depth chart for just offense/defense/special teams, which would kind of go hand-in-hand with this (so it's not all or nothing with that decision)
One thing you can do though to accomplish what you want to currently:
* Remove all the players from a position in the depth chart
* Do a player search. Choose the position you want to fill, and choose your team in the Team selection.
* Sort the result by "Max" instead of "Cur"
* Click on the players in the result set. You can see where they are currently in the depth chart.
* In the "details" tab of their player card, there's a link to "Assign into depth chart"
* When you assign into the depth chart, he will be added into the last spot. You'll be taken to the depth chart page.
* Go back in your browser to the search results, and continue with the next player.
Not quite as effortless as your suggestion but hopefully that will help in the mean time.