list manipulation - Why does my threaded function need to be substituted?

In my code I have

With[
 {
  rowCells=(genCells[#]&/@genSpecs[#])&/@clueRows,
  colCells=(genCells[#]&/@genSpecs[#])&/@clueCols
 },
 While[Not@isDone@Flatten@constraintTable,
    constraintTable=(Thread[f[rowCells,constraintTable]]/.f-> constraintStrip);
    constraintTable=(Thread[f[colCells,constraintTable\[Transpose]]]

                     /.f-> constraintStrip)\[Transpose];
 ]
]

but when I attempt to replace the substitutions for f with

With[
  {
   rowCells=(genCells[#]&/@genSpecs[#])&/@clueRows,
   colCells=(genCells[#]&/@genSpecs[#])&/@clueCols
  },

  While[Not@isDone@Flatten@constraintTable,
    constraintTable=(Thread[constraintStrip[rowCells,constraintTable]]);
    constraintTable=(Thread[constraintStrip[colCells,constraintTable\[Transpose]]]
                       /.f-> constraintStrip)\[Transpose];
  ]
]

I get

Transpose::nmtx: The first two levels of {Transpose[0],Transpose[0],Transpose[0],Transpose[0],Transpose[0],Transpose[0],Transpose[0],Transpose[0],Transpose[0],Transpose[0],Transpose[0],Transpose[0],Transpose[0],Transpose[0],Transpose[0],Transpose[0],Transpose[0],Transpose[0],Transpose[0],Transpose[0],Transpose[0],Transpose[0],Transpose[0],Transpose[0],Transpose[0]} cannot be transposed. >>
Transpose::nmtx: "The first two levels of {Transpose[],Transpose[],Transpose[],Transpose[],Transpose[],Transpose[],Transpose[],Transpose[],Transpose[],Transpose[],Transpose[],Transpose[],Transpose[],Transpose[],Transpose[],Transpose[],Transpose[],Transpose[],Transpose[],Transpose[],Transpose[],Transpose[],Transpose[],Transpose[],Transpose[]} cannot be transposed. \!\(\*ButtonBox[\">>\",

Why do I need to substitute in this way? How can avoid having to do so?

---

I have a similar issue with

showTable[t_]:=
Grid[
  Join[
    Join[
      ConstantArray["",{9,9},(Style[#,Bold]&/@PadLeft[#,9,""]&/@clueCols)]\[Transpose],
      (Thread[f[(Style[#,Bold]&/@PadLeft[#,9,""]&/@clueRows),

                (t/.cellGraphics)
               ]
    ]/.f->Join)
   ], 
   gridSpecs
];

where a substitution is also required in Thread to avoid errors.

Answer

If you want to avoid the substitution, it might be more "elegant" to use MapThread:

MapThread[Join, {colCells, constraintTable\[Transpose]}]

This works like Thread, but Join directly operates on the right arguments.