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?
I believe this question falls into the category of something that is context sensitive (like everything else in the UX world), but for a while it was definitely something that people believed to be true, and then there were evidence to suggest otherwise.
You can read about examples on UX Myth #3 - People Don't Scroll (i.e. only stuff above the fold counts) and see examples of why people do scroll if there is reason to do so.
However, since this Myth was established (and busted) a while ago, you may want to test this against your particular product or service just to make sure that the reasons for doing this makes sense for your audience.
You could create mockups with color designs that show ways to highlight the areas they want to have increased clicks on while maintaining a more user friendly website that is modern. Having a busy website also distracts the user rather than drawing their attention to the desired areas, which is another good point to bring up with management.
In the end, if it's their decision, all you can do is try to show them why you want what you want and convince them why it would be better.
Another good point is for responsive development, small headers can be difficult to see on smaller screens that are unable to use the zoom feature on their device, especially for less competent users, so that could push users away, depending on the target audience.