On most web development blogs (except for mine) you will find that marketing terms like conversion are used. This is because the primary purpose of web design, at least for many, is digital marketing.
If you are doing web design as a form of digital marketing, then it is necessary to make your website look good in the way "a good-looking website" is popularly defined. Otherwise, users will think your website is old, unmaintained, and low-effort, which leaves a bad impression on your business. The popular definition of "a good-looking website" generally corresponds to flat design, possibly with images and color-to-color gradients.
In every case, a primary purpose of web design should be to make it easy to access the content of a website. In order to access the content, you need to have a way of navigating to the content that users will understand.
It's advantageous to have a navigation experience that users know about, i.e. one that is popular. This way, your users already know how to navigate your website, having used other ones.
Sure, and I definitely advocate for innovation in web design. But an unpopular design can make your site look unprofessional and make it hard to navigate. Sticking with design norms is generally a good idea. If you have a new concept that isn't popular, then you may implement it; it might actually be good for user experience and marketing.
On the other hand, if you liked the old design seen in sites like Old Reddit and most sites made with Old Google Sites, and prefer it to modern design, you still shouldn't implement it because it makes your website appear unmaintained or low-effort to users, and it draws people away.