That, too, is primarily because of healers. In side skirmishes without healers, you can regularly see people fighting each other, rather than the ice, because they can kill each other on their own - And killing a DPS without a healer is fast enough to make it well worth it on its own, doubly so if you can reset the ice. With healers, people usually just focus the ice and disengage afterwards. The same frequently happens on large ice - if you come without healers, prepare to be attacked, only bots don't take advantage of that. With healers around, though, people just don't bother, if they fight at all, they fight after the ice is done, because killing anything takes way too long to be worth it.
You can put a bigger incentive on killing players in Shatter easily by transferring the ice credit of a player to the killer if you manage to kill a player. But I can already tell you that even that would not be enough to make people attack each other on the ice if healers are present - it's just never worth it.
And honestly, if League of Legends had healers of our caliber in their game, they'd never do anything but last-hit and attack towers either. Heck, the healers they have already caused similar issues in the laning phase back in the days. Soraka vs Sona, the infamous snoozefest of yore! And those never had more than a fraction of the power our healers have.
Expect every objective based mode to be similar to Shatter in that regard. Secure plays similar, PvP only happens when drones aren't up. And likewise in Seal Rock, when your tomelith is safe and no tomelith is gonna spawn soon. That isn't new. Rival Wings is gonna be similar and it doesn't even take the weird warmechs for that. And this is ONE part of why Morello once called dedicated healers toxic design, against much hate and ridicule from the community. I suggest you get used to it - it's gonna stay and possibly get worse.