Poor/wrong sampling in 1D DiscretizeRegion of splines?

There is a workaround involving Rationalize.

Jet0[pts0_: {{1, 0}, {1.8, 1.8}, {0, 2}}] := 
 Module[{xu, yu, n, m, knots, fx, fy, pr, mesh, t, r},
   pts=Rationalize[pts0,0.001];
  {xu, yu} = Transpose[pts];
  n = 2; m = Length[pts];
  knots = {ConstantArray[0, n + 1], Range[m - n - 1]/(m - n), 
     ConstantArray[1, n + 1]} // Flatten;
  fx[t_] = 
   xu.Table[BSplineBasis[{n, knots}, i - 1, t], {i, Length[pts]}];
  fy[t_] = 
   yu.Table[BSplineBasis[{n, knots}, i - 1, t], {i, Length[pts]}];
  pr = ParametricRegion[{{r fx[t], r fy[t]}, -1 <= t <= 1 && 
      0 <= r <= 1}, {t, r}];
  mesh = ToElementMesh[pr, "MaxBoundaryCellMeasure" -> 0.1];
  mesh["Wireframe"]]

works as expected:

 Jet0[{{1, 0}, {1.8, 1.8}, {0, 3}}]

DiscretizeRegion will work in place of ToElementMesh:

Jet0[pts_: {{1, 0}, {1.8, 1.8}, {0, 2}}] := 
 Module[{xu, yu, n, m, knots, fx, fy, pr, t, r},
  {xu, yu} = Transpose[pts];
  n = 2; m = Length[pts];
  knots = {ConstantArray[0, n + 1], Range[m - n - 1]/(m - n), 
     ConstantArray[1, n + 1]} // Flatten;
  fx[t_] = xu.Table[BSplineBasis[{n, knots}, i - 1, t], {i, Length[pts]}];
  fy[t_] = yu.Table[BSplineBasis[{n, knots}, i - 1, t], {i, Length[pts]}];
  pr = ParametricRegion[{{r fx[t], r fy[t]}, 0 <= t <= 1 && 0 <= r <= 1},
        {t, r}];
  DiscretizeRegion[pr, MaxCellMeasure -> {"Length" -> 0.1}]]

Jet0[{{1, 0}, {1.8, 1.8}, {0, 3}}]