I would find it really hard not having the left foot hi hat, would feel like i have to keep the ride more steady, whereas with a left foot hat you can vary up the ride a bit. At least that's how I find it.
A case can be made for the KISS (Keep It Simple Stupid) principle for all of us. The simplest set up you are comfortable with is just fine. Play with it and see where it leads you. Like others have suggested, though, hi-hats are essential in my mind for a lot of good reasons. In fact, a hit-hat alone can be absolutely magic in the right hands.
I'm with a few other posters... When I strip down my kit, I leave the hi hats and my ride for cymbals. No toms or crashes or frilly stuff. Actually, once it a while I like to use a hanging tom as a "low tom" in some of those setups.
Minimal kits are way more fun than huge ones. Pure fact that cannot be disputed by anyone, especially sticks4drums.