It’s not the same thing as welding, which is melting the plastic by heat.

Acetone is dissolving the plastic. It gets in between the polymer strands and untangles them so they float freely, and when it’s gone they settle back down into a solid with a different structure more like a salt crystal, and it tends to be harder and more brittle than the original plastic because you’re re-arranging the polymer strands in a different way than you’d do by welding with heat. There’s also a transition from two different polymer structures at the seam where the glue meets the bulk plastic, which becomes a weak point.

The second problem is that the solvent increases the volume of the solution, so the glue shrinks a lot as it dries. It dries fast at the outer edges and forms a seal, so the inside parts of the seam experience a vacuum as the acetone diffuses out, and that leaves bubbles in the glue.

So the joint between the two sheets becomes filled with tiny voids that compromize its strenght. In the picture I had glued ABS sheets together with the same plastic dissolved in acetone, and after some years I tore the seam apart, and that’s what it looks like in between.
Full of little holes.