There are two major reasons why we decided not to use a system of natural improvement like you propose.
As a general design goal, we want the player to have a certain amount of control over how his or her Battle Brothers develop. With natural improvement, that control could only be exercised in how the player employs Battle Brothers in combat situations, which creates a conflict of interests. On one hand, the player should want to fight as effectively as possible, and we want the player to have an experience that feels natural and (within the limitations of this being a 2d game and all that) be an immersive pseudo-medieval battle. Yet on the other hand, the player would be lured to change his or her tactics for the meta-gaming aspect of making optimal use of the system of natural improvement, e.g. risk the lives of Battle Brothers solely to increase their hitpoints in the long run.
A system of natural improvement requires substantially more effort in balancing to work well. It’s not insurmountable, but it is a part that can easily break and isn’t nearly as easily fixed, as even AAA games show (e.g. Skyrim). A system like this is easily exploitable, as you mentioned yourself, and the mindset that it comes with for many players would undermine the atmosphere and feeling of urgency and danger that we’re actively trying to establish.