I still see a lot of process improvement initiatives in organizations.
Leading to processes centers of excellence, improvement teams, Value Stream maps and fancy tools like process mining, 30-60-90 plans; all kind of stuff that should help to improve processes.
Sadly, I also still see that, after an enthusiastic start, all these initiatives might die a slow, theoretical, to-be dead.
I didn't do any scientific research, but I think that is caused by a misunderstanding about what "managing by process" is about, quite often.
As noted in other posts; I am pretty sure, your customers don't care that you are improving your processes.
They prefer that you execute your processes well; to deliver products and services that solve their problems.
So, processes are just a means, not a goal. A means to deliver product, services or solve problems for the (process) customers.
I've seen sometimes, when that's forgotten, that processes might end up in the hands of the improvement-enthusiasts, without a thorough awareness that only execution is what counts.
In theory, every process can be the best. But, happy customers don't exist in theory.
Oh yes, go ahead if you want to spend some time staring at process maps. But wouldn't it be an idea to start with making clear what stakeholders expect out of a process? What promise does the process have to deliver?
A delivered pizza within half an hour? An insurance policy with 0 mistakes? A machine that can run 2 years without maintenance? Those are all process results!
And maybe that raises awareness that a process is just a means. It should be "used" to deliver what you promise. So I would take that promise as a base to start process discussions. Making clear how well the process is performing. Try to make that process performance visible to anyone in the process.
And maybe then you discover process performance is not as desired.
And yes, maybe then we could draw some blocks and arrows on the wall.