How important are the Speaker Cabinets?

They are an integral part of the overall design so they are important. The overall design matters more than any particular cabinet shape or size. Generally, they should be very rigid, which infers greater weight. Larger cabinets cost more to build and maintain high rigidity compared to smaller.

One good example of a speaker cabinet built to the nth degree is probably that of the Magico mini, which is a rather small 2-way midsize monitor with integrated stands that cost over $30000. They can command that price not only due to good sound in a relatively compact package but build quality of the highest degree.

The volume of air inside (and porting) as well as stuffing will create a resonant system with the woofer. Cabinet volume and porting are matched to a particular driver. This is extremely important for the woofer.

Furthermore the edges and shape of the speaker may influence the edge diffraction of frequencies above about 500 Hz.

Furthermore cabinet resonances may color the sound and increase distortion.

the best cabinets are closed perfect cubes, no prorts or internal structurs. You can just stack as many as you want on atop the other. T walls must be free to resonate at 500 cylces thus use a thin copmpliant material. Make sure that no one slips any damping materials into the box .
The only downside is that they are a bit skittishhis cab be aproblem as some of the best made of really thin brittle material can break if it bunces off it's perch to the florr. If made right it will shatter. They make a really loud buzz /hum at 500 Hz.The family often gathers around to witness this like the first planes to break the spund barrier.
The pretyentious speaker makres use heavy damped non paralell walls to make them fancy. They add wieght with extra internal bracing -it's only purpose is to make the speaker real heavy and rthus feel like something substantial. That gives you the sense that they are a prestigious product.
Don't fall for that industry tomfoolry.