For the purposes of visualization, you want each cell to enclose approximately equal surface area. These are your "pixels". H3 is a way of rendering any subset of a sphere for display.
While squares have superior properties for analytical geospatial data processing that H3 doesn't have, such as congruency, they really only work for Euclidean spaces and the surface of a 2-sphere is non-Euclidean. Any system using squares will be a poor approximation of "equal area" relative to hexagons, which makes them poor for visualization. To use squares for indexing, you need an extra step that allows non-Euclidean space to be addressable from Euclidean space. There are two main ways of doing this.
First, one can project the surface of the sphere onto the surface of a Euclidean cube. Second, one can use an embedding, indexing the 2-sphere in Euclidean 3-space. Both of these can be trivially projected to a hexagonal system like H3 for visualization purposes and commonly are.
If you primarily need visualization and your data is small, using H3 eliminates the step where you need to figure out how to map non-Euclidean data models to Euclidean data models. If you are doing large-scale geospatial processing, it becomes worth the effort for both scalability and performance reasons.