The “Lauan” Plywood I got at Lowes is 0.1875 by my Mic. The Oak is a quarter, and is beefier, and much stronger when making a large toolbox. I would expect 1/8" wood would have nowhere near enough strength, For reasonable 3D, 1/8" wood is very difficult. I am currently engraving 1/2" material ~3/8 of an inch deep. It is very hard to do that in even quarter-inch wood 
Depending on both the nature and size of the job a tray for your restaurant bill and credit card looks very good in 1/8 but an 18"x24" serving tray (made on a pro) would look very flimsy even made from such a strong wood as wenge. It is all a matter of scale. This box material is over thick as it is very tiny…
But this …
several times bigger is not.
And this…
Would look downright silly with 1/8" material and even 3/8" would not look terrible. Though the grill looks good at 1/16".
For other things, even 1/8" can be too thick such as for marquetry, and I have found 1/16" Baltic birch great for hinges as I can tie more and smaller together spreading out the strain.
So having an open mind about what materials you use and their thickness will get you places rigid thinking will not,