Hi Summercat:
We tried that...but in most cases, it was not as much fun! Most of the time, the squares are contested. Also, the fact that the cards you are going to need are scarce forces you to plan ahead a bit. The game would be less challenging as turns progressed if you are only dealt cards that you can use. I like to use the analogy of tanks and infantry in WWII. At the start of the war, everyone had plenty of infantry, but tanks were in short supply. By 1944, everyone (Germany, the Soviets, the Western Allies) were desperately short of infantry, and had more tanks than they needed. A hand in a game like that would have all tanks...and you would be furiously discarding to find an infantry unit.
Thanks for playing.