Imagine you have a long line with marked zero point, and you shoot it from distance, then you check what point was hit. This is an analogy to selecting - at random - reaction. Now, each point hit (reaction selected) lies in some distance from the zero. It may happen that you have hit something very close to zero, but if you will measure it with higher precision you will usually see that you are still off. Same happens with reactions. In each reaction delta H (macroscopic effect) is effect on energy changes in the created/destroyed bonds and of all possible energy changes in interactions between molecules that exist before reaction and reaction. Just like hitting zero precisely is extremally unlikely (although you may get close), finding reaction in which all effets of all changes will exactly cancel out - is very unlikely, although not impossible.
Things get more complicated as in the real world delta H depends on the temperature reaction is taking place. But that's also a chance for us.
Reasonable approach will be to find reaction that is exothermic at one temperature and endothermic at the other, and then finding temperature in between. where delta H is zero. But IMHO such experiment will be futile, art for art's sake.