How to count the number of dates entered in a column using Numbers formula?

As described, the answer will always be 1.

It sounds like you're wanting your spreadsheet to count how many times the cell value was changed. It doesn't do that. When you change a cell value (e.g. set the 'last contacted' cell to today), all previous history of that cell is lost (other than via undo, which is inherently temporary).

The cell has no idea whether the current value is the first or thousandth value that's been entered.

The only ways to do what you describe is to either have a range of multiple cells with one date per cell (count the number of non-empty cells to see how many times you tried to contact them), or a separate cell that you manually increment each time you call.