How important is it to keep content above the fold?

The leadership at my company is constantly pushing to make heroes/headers thinner and thinner so that we can push more and more content above the fold. Consequently the website has a very busy, un-modern feel and all the heroes/headers look like ad banners. But they really only care about click metrics. Any advice on convincing them not to be afraid of larger heroes, and valuing an appealing look and feel over just click metrics?