Strange logic to make it a Saturday. How about a grateful Government move it to a weekday so at least the chaps and chapesses get a day to relax and celebrate.
Apparently Armed Forces Day is about the Public showing their appreciation for HM Forces by attending events where HM Forces give up their free time to march etc for their benefit - its not about us having a day off, even if the day is a Saturday in June. To add insult to injury, there is another Saturday in June when an awful lot of HM Forces work (Trooping the Colour).