To tidy up the previous post - if writing all the country meshes to a file has worked then at your convenience you can read it back into memory and access the elements of the Association rather quickly, possibly quickly enough for "production" work. Note that the time for a single country mesh from the previously defined "test" function (with a decent internet connection) is:

    Timing[test["Russia"]]  (* approx .5 seconds on my iMac *)

Now exit and launch a fresh session.

reg = Get["countrydata`"]; (* if the file countrydata.m was created, as above, load the Association reg into memory *)
Normal[reg][[All, 1]]  (* check that all 249 countries are there *)

Timing[reg["Russia"]] (* approx 10 microseconds on my iMac *)

So you get a nice speed gain, if you have enough memory:

MemoryInUse[]

325510952

I see the same odd behaviour as you all have seen but was able to get all the country mesh data by inserting it into an Association, as follows:

Countries = #[[2]] & /@ 
   EntityList[EntityClass["Country", "Countries"]] ;
 test[country_] := Module[{polygons, meshes}, 
  polygons = Entity["Country", country]["Polygon"][[1, 1]];
  meshes = 
   BoundaryMeshRegion[#, Line[Join[Range[Length[#]], {1}]]] & /@ 
    polygons;
  TriangulateMesh[RegionUnion @@ meshes, MaxCellMeasure -> 5]] ;

reg = Association[Map[(# -> test[#] ) &, Countries]];  (* runs in 34 seconds on my iMac running MMA v12.1.1 *)

Put[reg, "countrydata.m"]  (* saves all meshes in a file, about 168
MB *)

{reg["France"], reg["Canada"], 
 reg["Iceland"]} (* read a few meshes out of memory *)

This sometimes works and sometimes kills the Kernel so the underlying trouble is still here.

Mac OSX 10.15.5

Mathematica "12.1.0 for Mac OS X x86 (64-bit) (March 18, 2020)"