I am new to the game, bought the core box recently. After having watched a bunch of gameplay videos, and tried a few hands, my question is: why would anyone want to attack several objectives in 1 turn, instead of committing all their attackers to bursting a single one?

Welcome to the game!

The short answer is that it’s very situation dependent. Long answer, by attacking multiple times, you can make your opponent have to worry about blocking multiple engagements. This can get you more bang for you buck with various combat tricks. Alternatively, if some of those are unopposed, you do more total damage by getting an extra unopposed bonus or 2.

On the other hand, you leave your opponent the ability to use cards that remove damage from objectives. So in some instances it’s definitely better to not leave damage sitting around.

Also, for what it’s worth, most of the community uses the forums on cardgamedb.com over these forums. You’ll get more views and answers there than here.

Late game force your opponent into inefficient defensive maneuvers. Sure, you can send all you units in a massive push, but you can't hide that and you can't effectively get your opponent to waste cards in Edge.

Seeing Yularen sucks, yeah, but I still think spreading damage around is the better overall play.

There are also times where you are content to let a given objective hang around for a little bit longer. Perhaps you know or suspect that your opponent is running some other objectives that have effects that would be very bad for you. It might be better to sprinkle the damage around early and then go for multiple objectives in a single turn down the road.

There is also the math of the situation and not "wasting" objective damage. If you have an objective with only a single hit point remaining, you can go at it with almost anything a lot of times. Maybe let one of your heavy hitters do some massive damage to one objective and leave one unit back, doing some nice significant damage on another objective. Then, your opponent is very fragile in the later game, as you can start blowing up objectives even with smaller, less significant units.