You don’t need a flashy site if you already have the reputation. But without other signals an old simple site will be interpreted by many as an indicator of something amateurish or outdated.
I once raised a seed round with a dirt-simple (deliberately) deck that was just black and white text, Times New Roman default powerpoint style with zero design elements other than bullet points.
I got a lot of comments about how refreshing it was to just let the ideas and data stand for themselves without frills.
I accept that a deck and a website are not the same thing, but there is value in sometimes deliberately under-designing something.
But sometimes there's so much flash that you can't even tell what's being sold. And then there is the immediate blatant pop-over that demands that you make an account before you even have a chance to see the product.
Who designs crap like that?
Restaurant websites should be a readable pdf of the menu and prices and operating hours with a link for further information about the restaurant.