What exactly would this do that isn't done now?
Actually it can save you from some clicks. If you see a system with one(ore more) fleeticon(s), you could easily click the star and get at a glance displayed what planets and what fleets there are.
While currently, you'll need at least 2 clicks(or more, depending on whether there are enemy ships too).
In the perfect world we'll have infinitely large screens and the abilitiy to show all possible information on the sidepanel. Unfortunately we have limited screen area to use, so need to be selective about what is shown where. If we put a bunch of fleet info on the sidepanel, then we have to show less other information. This will me we'll need a scrollbar to see additional planets more often, or we won't be able to put as much cultural or buildings or economic information on the sidepanel. Since there is already a fleets window, which they player can click open if they want fleets information, just the ability to save a click isn't a very strong argument. Sure, you could save a click in cases where you need to see both fleet and planets, but the current design is based around the idea that you'll probably want one or the other as often or more than you'll need both about the same system at once. Keep in mind that it also might mean extra clicks to put fleet stuff on the sidepanel, as you'll have to displace other useful system/planet info.
There's also enough on the sidepanel with the system info and individual planets info already not to want to devote more space to fleets info as well.
Who decides what 'enough' is? In my opinion there is pretty less info on the sidepanel at the moment.
You asked me, so I told you what I thought. However, I meant more so enough that needs to go on the sidepanel about planets than what's there now. Presently the sidepanel sucks and needs a redsign in order to show enough info about planets... I've tried to do this, but it's mostly been ignored. Needed things include meter values, max meter values, old meter values, expected meter value changes, resource production, population, max population, growth, race, environment, size, specials, buildings (name, status, basic info about, perhaps some control widgets if applicable, maintenance costs of, icon/picture of), happiness/morale levels, construction meter info, health meter info, faction / cultureal info, etc. should all be visible without having to open a sub-screen about the individual planet. There also needs to be UI widgets to manipulate this stuff, which is more space-consuming that just displaying the info.
There's nothing particularly troubling about a "fleets at this system" button that opens the appropriate fleet window, though. This would be relatively small, and I posted a feature request
for it quite a while ago.
Even better might be to show multiple fleet icons on the map, with different icons to indicate info about the fleets, such as size or role or class of the ships in the fleet, or perhaps a small number indicating how many ships or some abstract ship-value rating for the fleet... or the fleet's visibibility / stealth, etc.