Seems like that might be a little cheaper than developing ECM to target drones. Although if it is really just a pork-barrel, then a $200 shotgun with $25 worth of shells is much less efficient than a multi-thousand dollar radar jammer rifle.
Effective range for taking out a drone is "as far as the bird shot will shoot" which is much further than ~120ft. We aren't talking about effective range (e.g "breaking a clay plate").
That being said - your point about increasing altitude still stands. I'm not sure how birdshot will go when shot near vertically - but it can travel well over 200 yards horizontally depending on if you're using 04 or 08, etc. At a certain point its harmless to humans unless it hits in the eye but as long as it hits a blade of a drone it could still damage the drone and bring it down. It doesn't need to completely destroy the drone like a point blank blast of a double barrel with buckshot would.
In a situation like a max-security prison, where you've already got cleared dead spaces around it to shoot escaping prisoners, its not really an issue.