I have done both some home photochemical PCB etching and some vinyl cutting but not that specific combination.

As photo mask it makes little sense in most cases. Just buying a transparency which can be used in an inkjet printer will likely be faster, easier and produce better resolution. These used to be widely available due to use in overhead projectors in schools and offices, but still shouldn't be too hard to get due to use when screen printing custom t-shirts.

As a direct physical resist it makes a bit more sense since it would allow skipping one chemical bath and the photo transfer process. I have seen some people online having very good results of it for decorative etches with moderate size details on thicker metal parts and glass. But I am somewhat skeptical about it withstanding full depth cutting of very fine grids with high pressure circulation like the one demonstrated in Applied Science video. It will likely come down to etching depth (is it a metal sheet 0.2-1mm or the copper layer on PCB 0.035mm or decorative surface etch), how aggressive your liquid circulation is, type of vinyl and it's adhesive (ones designed for outdoor use might be more resistant to liquid for longer), size of details. With concentrated enough etching liquid allowing fast etches, mild agitation and wide enough lines (>1mm) the vinyl should hold up.

In the worst case if adhesion during etching turns out to be a problem it should still be possible to use the vinyl as stencil while painting on whatever paint to be used as resist. This should still be much faster than doing photo step.

One of the good parts of photochemical manufacturing is that you can make something like a mesh with hundreds of tiny holes that would be impractical with any other approach. It doesn't matter how complex the pattern is. While you might be able to cut such patterns on vinyl cutter worst case by leaving machine to work for few hours, weeding it might be a big problem. After cutting you need to manually peel half of image you don't want (called weeding). For simple large shapes it's not a big deal but for complex cuts that have a lot of holes or maze like structure it can be quite time consuming. There are industrial cutters that can do the weeding automatically, but I don't think any hobby level machines like Cricut have this feature.

If you have something like a mesh and you are removing mesh part leaving only the tiny dots or pattern with thin long unsupported lines (like a PCB), you need to be very careful to avoid accidentally nudging and separating the small details. This can happen during weeding, transfer to target material and even cutting (for some types of materials). The last one was major problem when I tried cutting copper tape directly, original backing tape was just too slippery, less of a problem for suitable vinyl.

None of that gives you hard answer, but I hope my experience was of some use to you.

laser cutters seem better on the software side, but more expensive, less safe? (and also not safe at all for vinyl)

[1] https://uscutter.com/hp-latex-54-basic-plus-cutting-solution...

These just look like signs. (But cool nonetheless.)

(Maybe it is easy to do in OpenSCAD?)