Most logos were designed to be printed. The question that matters more: how does it look at 32 by 32 pixels in a browser tab?
The Favicon Test
If you cannot reduce your logo to a recognisable favicon, it is not optimised for digital contexts. Complex logos with intricate detail degrade at small sizes.
Responsive Logo Systems
Modern brand systems use responsive logos ÔÇö different marks for different contexts. A full wordmark for large applications, a simplified version for medium, an icon-only mark for the smallest sizes. Slack, Airbnb, and Google all use this approach.