A gantry may not be required in the future. A gantry is used because it greatly simplifies the problem. The gantry allows a fixed known relationship between the print head, the ground, and what is being printed. A simple 3D printer can work completely blind.

But this need not be the only way to 3d print. It's pointless to have a mobile 3D printer for desktop printing applications. But construction? The case may be different. Imagine a swarm of small robots, each a small cement mixer and print head. Hell, as absurd as it sounds, little flying printing drones might turn out to be a viable solution. The tech required for these is way beyond what is needed for a conventional fixed 3D printer. But it's probably possible. You don't set up a huge gantry for your giant house-sized 3D printer. Instead, you unleash a swarm of printing bots onto a construction site. They build up the house like bees assembling a hive from their own wax.

Now you might wonder if this could ever be financially viable. A swarm of printing robots? Well, historically, nothing changes technology faster than war. War forces innovation by necessity. Countries are getting really good at making absurd numbers of high quality robots cheaply.

For example, what's going to happen to all the Ukrainian drone engineers once the war ends? Sure, some will stay in the defense industry, but peacetime defense budgets are always lower than those of a nation facing existential war. Imagine the minds that are currently inventing drones that can fly a hundred miles and autonomously hunt down and kill individual enemy soldiers. Apply minds like that to the construction automation problem, and suddenly a lot of doors open up.

I mean, without commenting on the state ore potential of 3D printing homes, american paper homes would not be the comparison I'd make. The prints are made of concrete, so I'd rather compare it to european housing (I don't know enough about construction in asian or oceanic regions to compare it to anything there).