Time is not a 'dimension' in the same way I would describe a spatial 'dimension though.

In a spatial dimension you are presumably free to to choose any direction, think of it as a flat paper to see how I mean. But 'time', or its 'arrow' to express it clearer, has only one direction. so it's not really the same. As degrees of freedom though it becomes slightly more unclear, as I think. Because thinking that way I don't think it matters what 'directions' you give a degree of freedom. A length is just a length, it's a degree of freedom, as a width can be seen as another. This is from looking at a combination of degrees of freedom, as the way we once started from, defining those 'singular dimensions', we might expect

Alternatively, I think you can use the same argument, that the three spatial degrees allow for any direction, going out from some defined origin, in that 'plane'. But the temporal degree of freedom has only one direction, as far as we can measure experimentally.

What one should consider is that length, width, and height, has its original definition from the world we exist in. Any piece of matter will present us with those definitions, looking and measuring. Imaginatively though, you should be able to interchange any of those spatial descriptions, as a length for a width, finding it to express the exact same.

So what makes sense from defining dimensions from a piece of matter becomes trickier if you look for how to define each spatial dimensions 'uniqueness'. They should be interchangeable as I see it, as they will imaginatively, each one treated as a isolated degree of freedom, become the exact same in form of the description you then can make.

But the arrow will still be unique.