I don'y build light frigates late game, becuase a Kodiak, a Destra, or a Enforcer would destroy them in a few shots, so unless you plan on building a lot of them, which is not a cost effective way to kill capital ships or LRFs, they're useless. Just stick with LRFs, HCs, and Capital Ships with Carriers and Support ships late game.

They are obsoleted by people spamming missile frigates, but that in turns get obsoleted by carrier cruisers. As fleet composition becomes more balanced and support cruisers start showing up, light frigates come back into their own because they are cheap, do good damage and severely impair the function of support cruisers.

i mean, if the opponent brings a lot of Overseers or Subjagators to a fight, that can really change the whole dynamic and Light Frigates are the best counters.

A light frigate is also about as tough against bombers as a heavy cruiser is, and for far cheaper. 

The other advantage of light frigates is that their weapon research appears low on the tree while heavy cruisers tend to use more advanced weaponry.

Finally, in a siege situation they are against reasonably resistant to strike craft while building much faster than heavies.

Light Frigates are still quite cost effective when massed. Especially if you need to split your army up.

Tactically speaking, it's far more annoying to focus fire on a bunch of small ships that keep retreating (due to user micromanaging) than a few big, slow ones. Thus, cobalts can actually be as hard to take down as kodiaks, for less cost. In a team game, cobalts benefit from the Halcyon's Amplify Energy Aura, whereas the kodiaks have no relavent aura.

Destras are probably a better choice than disciples however, due to their area of effect attack, and the overall weakness of disciples.

Vasari light frigates are beasts when upgraded. They can repair while being focused on and hold on much longer than cobalts or disciples. Enforcers can too, but having them sit around means sacrificing a larger comparitive portion of your army.

Fear the mighty Cobalts-only fleets!

Aye, especially as of 1.1. With the increase in importance of carriers, light frigates are even more important opnce you have their higher level abilities researched.