Beware this goal. I'm dealing with the consequences of TDD taken way too far right now. Someone apparently had this same idea.
> management who do not fully understand the problem nor are incentivized to understand it
They are definitely incentivized to understand the problem. However the developers often take it upon themselves to deceive management. This happens to be their incentive. The longer they can hoodwink leadership, the longer they can pad their resume and otherwise play around in corporate Narnia.
It's amazing how far you can bullshit leaders under the pretense of how proper and cultured things like TDD are. There are compelling metrics and it has a very number-go-up feel to it. It's really easy to pervert all other aspects of the design such that they serve at the altar of TDD.
Integration testing is the only testing that matters to the customer. No one cares if your user service works flawlessly with fake everything being plugged into it. I've never seen it not come off like someone playing sim city or factorio with the codebase in the end.