The original note, as written at the time
Consider micro bricks with magnetisable cores. A powerful, focused and versatile magnetic field is used to propel and align the micro bricks in their desired positions. This way an entire building or part of a building can be constructed quite easily. The micro bricks have meshes that connect them with each other and other elements. A form of cheap cementitious or other binder is ejected from within the microbrick when it is in place.
Ongoing development
Micro bricks with magnetisable cores, propelled and aligned into position by a powerful, focused, versatile magnetic field. The bricks have meshes that connect them to each other, and a cheap cementitious binder is ejected from within the brick when it is placed.
The mesh is the detail that makes this a construction system rather than a demonstration. Magnetic placement alone gives you a pile of small objects in a shape. Interlocking meshes plus a binder gives you a wall, and the binder firing from inside the unit means the joint forms at the moment of placement, before the field releases.
What this changes is the labour model. A mason places units by hand, at a rate limited by reach and fatigue, and the scaffold exists so the hand can get there. A field places units without a hand, so the constraint moves from the person to the field generator, and a wall can be built from the inside out.
The scale problem is the interesting one. Magnetic force falls off sharply with distance, so a field strong enough to place a brick accurately is a field that is small and local, which means the machine is a head on a gantry after all — and then the advantage over printing is that the material is masonry rather than paste.
The honest place for it is small and repetitive: a boundary wall, a drainage channel, a retaining block. Anywhere the same unit is repeated hundreds of times and the design is already decided.
Robots are bad at buildings because buildings are irregular. Make the unit small and regular, and the irregularity comes out in the assembly.