If you have multiple webplayer tabs open in your browser, all showing Spotfire analyses, they all use the same icon (favicon).
To end-users, these different analysis files may be more like "applications", and it makes sense to have individual icons in the browser tabs to represent different applications.
For example, a company may have a couple of production-ready status dashboards, some analysis files used for digging into data according to some guided workflow, and then the end-user may have created something ad-hoc.
Having individual icons for these could potentially save a little bit of time and confusion on the end-user's part, and could also be a part of brand/styling on a more fine-grained level than cobranding.
(Compare to Library thumbnails that you can set per-analysis already today.)