I used to do a lot of optics calculations…
So one of the cool things about lasers is that it’s “coherent light” which means that it is all phase aligned, and all one wavelength. This means no refractory errors with focal lengths, and no weird interference issues. So on the surface, your idea makes sense. You avoid diffraction patterns, and even standing wave interference.
In the real world, not so much. The precision required is actually kind of terrifying, because jt has to propogate all the way back to the laser tube itself.
So the focusing lens takes collimated laser light from the tube and focuses it to a point, but everything about that light source is still present in the focal point. A minute variation in the alignment of the beam or any mirror in the beam path is still present at that focal point. So long as the laser strikes the focussing lens, the focal point remains fixed relative to the lens, although the absolute value of any error in alignment from the tube to the lens is still present, and it remains present if you then collimate the beam.
This means that any error in that alignment gets magnified in the output vector of the beam by a factor of the distance from the lens to the error divided by the focal distance of the lens.
A vibration causing the beam to wiggle by 1mm at the lens (let’s say for argument the first mirror) would be an error of maybe 2.5m distance with 1mm deflection, that is something like 0.02° vibration. You’d be able to see it, but you’d nesd to concentrate. The resulting deflection in the collimated post focal beam, however would be 1.13°. It may not sound like much, but such errors are cumulative, and it doesn’t take long before your laser makes “straight lines” that look like they were drawn by engineers on the back of a napkin after their 40th beer.
Also, we don’t get theoretically perfect materials. We get real-world materials. Transmission of light always has reflection and absorbtion. Absorbtion over the beam radius (~6mm typical) still gets the glass a little warm in that spot. Make that radius 0.1mm, and the energy gradient gets a little crazy. Like @jeffeb3 said, those lenses ain’t gonna last long.
(I went back to this because it’s been a while since I had an optics thought experiment to go through.)