For example, here are top five accounts in each site (this picture was taken when I was in Biology SE).
As you can see, all the badges are DNA, while Academia's badges should be hats, so on.
What do you think?
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I share Tim Post opinion that it would be nice to have, however not so simple to achieve due to technical issues.
Each site has its own CSS Sprites which contains most, if not all, icons used in the site e.g. vote arrows, badge icons, and more. For example, the sprites for MSE is https://meta.stackexchange.com/content/stackexchangemeta/img/sprites.svg.
Now in order to include all the badge icons from all sites in each site, you will have to load all those sprites, from all sites, on each page load of the profile page, or to create one "super sprites" with all the icons from all sites. Both of these are not really feasible, hence this request will most likely be declined, or delayed until some major change is done in the way badge icons are handled.
We're already loading all the icons for the websites, as seen on the left side of the screenshot in the question. Where are those being stored? Can't the badges be stored the same way?
Also, why do separate gold, bronze, and silver badges exist for each website? Wouldn't it be easier just define one template and then apply a filter to it on the client end to generate the proper color?