There are many ways to bring some order back into the world, as you say, but it can be a struggle. In my experience, business leaders will support simpler systems and processes if (and only if!) the benefits clearly outweigh the costs.

As an IT professional, framing the right perspective is essential to getting acceptance for better systems. Presenting a more powerful, but simpler, system as "losing some rarely used and inefficient features" is a sure way to get that project rejected. Management will only hear the "losing" part as a loss in total value and therefore worse than the current solution.

Personally, I like to present formalized system upgrades as the price of growth and future growth potential. Most business leaders can wrap their heads around the concept of "we need to focus and streamline in order to reach the next level", regardless of technical experience.