{
        packages.zlib1 = (pkgs.haskellPackages.zlib).override { zlib = pkgs.zlib; };
        # it works
        packages.zlib2 = (pkgs.haskellPackages.callCabal2nix "zlib" inputs.zlib-src { }).override { zlib = pkgs.zlib; };
        # it works
        packages.splitmix1 = (pkgs.haskellPackages.splitmix).override { testu01 = null; };
        # it doesn't work
        packages.splitmix2 = (pkgs.haskellPackages.callCabal2nix "splitmix" inputs.splitmix-src { }).override { testu01 = null; };
      };

Only the last one failed with 'error: function 'anonymous lambda' called without required argument 'testu01''

{
        packages.zlib1 = (pkgs.haskellPackages.zlib).override { zlib = pkgs.zlib; };
        # it works
        packages.zlib2 = (pkgs.haskellPackages.callCabal2nix "zlib" inputs.zlib-src { }).override { zlib = pkgs.zlib; };
        # it works
        packages.splitmix1 = (pkgs.haskellPackages.splitmix).override { testu01 = null; };
        # it doesn't work
        packages.splitmix2 = (pkgs.haskellPackages.callCabal2nix "splitmix" inputs.splitmix-src { }).override { testu01 = null; };
      };

Only the last one failed with error: function 'anonymous lambda' called without required argument 'testu01'

cabal2nix --system x86_64-linux https://hackage.haskell.org/package/splitmix-0.1.3.1.tar.gz gives me

{ mkDerivation, async, base, base-compat-batteries, bytestring
, containers, criterion, deepseq, fetchzip, HUnit, lib
, math-functions, process, random, template-haskell, test-framework
, test-framework-hunit, testu01, tf-random, vector
}:
mkDerivation {
  pname = "splitmix";
  version = "0.1.3.1";
  src = fetchzip {
    url = "https://hackage.haskell.org/package/splitmix-0.1.3.1.tar.gz";
    sha256 = "0mll5axdvh5wan6prh3v6l2n15xsj31ghi0g887ljpk515id5a2w";
  };
  libraryHaskellDepends = [ base deepseq ];
  testHaskellDepends = [
    async base base-compat-batteries bytestring containers deepseq
    HUnit math-functions process random template-haskell test-framework
    test-framework-hunit tf-random vector
  ];
  testSystemDepends = [ testu01 ];
  benchmarkHaskellDepends = [
    base containers criterion random tf-random
  ];
  description = "Fast Splittable PRNG";
  license = lib.licenses.bsd3;
}

So this looks fine.

The problem with override is that it depends on initially computing the derivation successfully. This doesn't work if an argument is missing which is the case here with testu01. That's why callCabal2nix has a third argument to pass in arguments (which can also act as an override at the definition site). So you want to do:

(pkgs.haskellPackages.callCabal2nix "splitmix" (builtins.fetchTarball "https://hackage.haskell.org/package/splitmix-0.1.3.1.tar.gz") { testu01 = null /* just pass something */; }).override { testu01 = /* later we can pass something else: */ my-pkg; }