Change mesh density of Graphics3D object made of Triangles

I am new to mesh discretisation on Mathematica. I have a Graphics3D object made up of Triangles, that I would like to convert into a MeshRegion object using DiscretizeGraphics (see https://reference.wolfram.com/language/ref/DiscretizeGraphics.html).

In particular, I would like to control the mesh density. The above link tells me to use the MaxCellMeasure option, but it doesn’t seem to make any difference to my graphics!

Thus,

Table[DiscretizeGraphics[g,    MaxCellMeasure -> {"Area" -> m}], {m, {0.3, 0.01, 0.001}}] 

gives: enter image description here

As you can see, the meshing is unchanged. It doesn’t matter if I replace "Area" by "Volume" or "Length".

Can someone please tell me how to do this properly? Is this happening because my Graphics is already made up of triangles?