You can change things but you must do it. You must put your reputation at risk, expense time that you wont be compensated for, go through conflicts you'd rather avoid, make lifelong enemies wether you succeed or not. Then, you changed the rigid structure once more and the next guy will either try to put it back where it was and face less resistance or fold it one more time and face even more.
You cannot teach a rigid structure agility just like you cannot teach iron to be silk, and the structure is rigid for a reason: size, cost, regulation, cultural beliefs, rot due to time, past mistakes (in my experience the largest factor: a mistake 10 years ago can justify 3 days a week of useless processes today) etc. You can change the structure but it's CEO-level work to change its rigidity.