Unfortunately, that's the technique that has given mesh a bad rep. If you stick it to the wall, the mud doesn't get under it, and it can delaminate the patch, and doesn't adhere well.
Properly used, you mud the wall (just like with paper tape), and then embed the mesh in it. The strength of the mesh is in combination with the mud, it makes a composite material, similar to steel reinforced concrete as opposed to plain concrete.
However, mesh tape is not a substitute for paper tape. Paper tape is the appropriate material for most seams. Mesh is applicable to thick sections, uneven sections, patch and repair, and sections that may move slightly and tear the paper. In those cases, it's performance exceeds paper. For taping simple seams, it is an inferior material, and often used by amateurs like you describe above, by sticking it to the wall. It keeps them from having to learn how to properly prep and embed paper tape. But, degrades the overall performance compared to properly applied paper.
It's not a paper - good, mesh - bad simple equation. Both have their suited uses, and need to be used appropriately.
The shear strength of paper to resist shrinkage cracking is greatly over-rated. If you get shrinkage/expansion in the structure, it will tear the paper at the joint, as that's the weakest link. It would also tear mesh, although it might retain some integrity across the crack. If you are able to restrain the joint by how you screw the drywall down to the studs/rafters/trusses, the sheetrock itself will crack somewhere. No kind of tape is able to resist this type of failure.