Technically not important at all from a search and discovery standpoint, but they are VERY important from a branding standpoint.
In some areas the audience will NEVER see the banner, but in some other areas (possibly brands?) a well designed banner shows a visual, professional authority. A business trying to present themselves as a professional company, such as realestate, a company that uses youtube to demonstrate products, a professional giving advice on a variety of topics, will want a well designed banner so they look like they know what they're doing.
A company that has a banner that looks like it's been done by a teenager using MS Word would make me question their professionalism. If they can't get their branding to look professional, or can't afford to find a decent designer, why should I trust them to take anything in their business seriously? If they can't afford a decent designer, how can I trust they're good enough in their profession to make any sales/revenue in what they do?
To the vast marority of folks watching it won't matter at all, but on an overall scale, it's a part of the overall image and brand, and it starts becoming very important after a while.