How important is wire mesh in a concrete floor

Personally, I'd go for a bit more than 3" of concrete if you're putting a vehicle on it, that would be OK for a footpath, but not really for anything more. Personally, I'd double that, but that may be overkill.
And yes, mesh is important:

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Concrete is strong in compression, but not under tension. So, if it flexes, like a slab with a vehicle on top of will do, it cracks at the bottom whre the flexing becomes tension. Steel mesh will prevent this to a large degree and hold it all together. This is why the mesh should sit closer to the bottom.

"Get the mesh cut into bits, then wire it together"
That's what I would do. Or more likely get it delivered, with my ballast and cement.

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I could go on about this adinfinitum (I've got qualifications in concrete &#; Yawn!) but I won't&#;. &#;

It's a common misconception that rebar increases the load bearing capacity of a slab on grade. The reality is that a 4 or 5" slab isn't deep enough to take advantage of rebar's tensile strength and make the slab act like a beam and span between supports.

Firstly, by the time you allow an 1 1/2" of cover under the mat, it's essentially in the middle of the slab where there isn't any tension to resist. Secondly, even if this theory is correct, what happens around the perimeter where the slab cantilevers and the top is in tension.

The reality is that a slab on grade is not structural and simply bends and transfers the loads placed on it to the soils below. If those soils give, your slab is going to crack. You need to get into much thicker sections before you get a true structural slab.

For a slab on grade placed on a solid base constrained by perimeter walls, there is no absolute need for rebar. I have placed many hundreds of thousands of square feet of such slabs on engineered commercial and industrial projects over the last 30 years. Now a free floating mono slab is another matter. Rebar would be helpful here, not to prevent cracks but to hold everything together if the slab experiences some movement.

Rebar's only function in a slab on grade is to keep cracks from opening up. In fact rebar actually increases the likelihood of shrinkage cracks by restraining the slab from shrinking inward as it drys. Think of rebar as crack control not crack prevention.

Finally, to say that the absence of rebar somehow implies a contractor is inept is a ridiculous statement. There a many reasons including the owners specifications and budget that could determine whether rebar is installed.

I realize this flies in the face of conventional wisdom and our dearly held belief in overkill but we might as well pass on accurate information to those who come looking.

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