"Code hygiene" is not a goal but the means to a goal. The reason hygiene is good is that ideally should (1) enable you to ship faster and (2) have fewer bugs so you can focus on shipping the next thing instead.
So then there's two options - if your hygiene doesn't give you (1) and (2) then it's pointless. On the other hand, if you do have a velocity issue because of bad hygiene, then that sounds in line with your c-suite concern.
"hey boss, our code needs to be more hygienic" - nobody cares.
"hey boss, we are at 10% of possible velocity because of issues X,Y,Z, and we can be 10X faster if we take a month to fix those" - now they are listening.
So we offered a solution to our customers, and then we could customize this by offering our own "consultant" developers. In the end, each developer had a goal to be "80% of their time billable".
Now we sometimes had to write these things called "channels", which took about 2 weeks to write. If we would have rewritten the framework behind it (which would take about 2 weeks) we could have probably sped up writing channels to less than a week! The thing was, nobody really cared if it took 2 weeks or less than a week, since the customer paid for it. My statement of 'let the customer pay for the 2 weeks anyway' never got hold (that would have probably resulted in some accountant fraud I guess, the way they set up the contract). So anyway, nobody was willing to invest this 2 weeks refactoring that would almost instantly pay itself back.
We were writing channels all the time, and it always felt like such a waste.
Sometimes in corporations, you can end up in the most crazy situations. I've seen plenty.