Solve matrix of ODEs using NDSolve

Question

I wish to solve an ordinary differential equation of matrices. This is a minimal working example I am working towards nonlinear equations. The accuracy of the solution is important for me. I have hit two problems.

1. Why does Mathematica have to set up differential-algebraic equations?
2. For accuracy how can I use something like the options; InterpolationOrder->All, Method->"ImplicitRungeKutta"?

I generate a set of three differential equations, their initial conditions and then go on to solve them using NDSolve

ClearAll[d, v, t];
ff0 = {10, 15, 22};
mm0 = {1, 2, 2.5};
dr = {0.001, 0.01, 0.015};
nn = Length[ff0];
SeedRandom[123];
R0 = Orthogonalize[RandomReal[{-1, 1}, {nn, nn}]];
R = Orthogonalize[RandomReal[{-1, 1}, {nn, nn}]];
cc = R0 . DiagonalMatrix[2 dr 2 \[Pi] ff0 ] . Transpose[R0];
mm = R . DiagonalMatrix[mm0] . Transpose[R];
kk = R . DiagonalMatrix[(2 \[Pi] ff0)^2 mm0] . Transpose[R];
(* Initial conditions *)
dic = ConstantArray[0, nn]; dic[[1]] = 1;
vic = ConstantArray[0, nn];
(* Solve differential equations *)
te = 30;
{disp, vel} = {d, v} /. First@NDSolve [{
     d'[t] == v[t],
     mm . v'[t] + cc . v[t] + kk . d[t] == 0,
     d[0] == dic, v[0] == vic},
    {d, v},
    {t, 0, te}]

This does work and gives me answers but the following message appears

NDSolve::ntdvdae: Cannot solve to find an explicit formula for the derivatives. NDSolve will try solving the system as differential-algebraic equations.

Why is Mathematica doing this?

If I try for high accuracy using

(* Solve differential equations with high accuracy *)
te = 30;
{disp, vel} = {d, v} /. First@NDSolve [{
     d'[t] == v[t],
     mm . v'[t] + cc . v[t] + kk . d[t] == 0,
     d[0] == dic, v[0] == vic},
    {d, v},
    {t, 0, te},
    InterpolationOrder -> All,
    Method -> "ImplicitRungeKutta"]

Then I get a string of messages with these being key

NDSolve::ntdvdae: Cannot solve to find an explicit formula for the derivatives. NDSolve will try solving the system as differential-algebraic equations.
NDSolve::nodae: The method NDSolve`ImplicitRungeKutta is not currently implemented to solve differential-algebraic equations. Use Method -> Automatic instead.

I am using version 14.0.0 for windows.

Thanks for any help