I will do open toes for very casual, flat sandals though the front strapping has to be fairly wide and in just the right place.
For a dressy "sandal" or summer shoe look I really have to go closed toe, not just for bunion-toe issues but because indoors, even in summer, I will wear very sheer nude hose. So I look for closed-toe but strap, slingback, or some other area of openness.

I wear the keens in #1 for hiking and walking my dog in the summer. I have worked in places where we had to wear covered footwear. However, I am one of those that think feet are sexy and the more of the foot you show the better.

I think you look great in #3. I love caged shoes.

I don't show my toes either - and I do like my feet and have regular pedicures. Like you, I simply prefer the look of closed toe shoes - but don't mind them open on other areas of the foot at all.