We all know how something would work better. So, start by writing that at least. Everyone's favourite timepass is giving advice, so, simply take it for you systems.

You will find it's easier and effective to lead your team into better and better systems by scratching their current itches. They'll be thankful, and that much more open to something even better.

It's like leaving them breadcrumbs to the better.

Without this, you anyway need to align them to an completely new system. Most people resist.

Therefore, it's better to build them up step by step towards what's best, like a good movie moves you to climax!