I've been taking advantage of my high strength and picking up every crate I've come across. They weigh so little.
I've been using them to set up bottle necks/choke points so enemies can't get the number advantage on me. It's really effective for just about every battle.
I feel like it's a really cool tactic that should, at best, slow enemies down. The way it currently works makes the game way too easy. You can box enemies in and they will simply pass their turn, eliminating the entire challenge.
Enemies should have enough AI to realize that they are trapped and should spend AP removing them from their path.