Why do adjacent cells in Excel display the same cell address when using the formula '=cell("address")'? Is it not expected for them to have unique addresses?

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This is because the formula '=cell("address")' returns the address of the current cell which is relative to the active cell. So when the formula is entered into an adjacent cell, it will return the same address as the active cell. If you want to get the unique address of a cell, you can use the absolute reference by adding the '$' symbol before the column and row reference in the formula. For example, the formula '=cell("address", $A$1)' would always return the address of cell A1 regardless of which cell it is entered into.