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Time and distance are 2 different things, yes they are both dimensions but the size of one "unit" of time isn't linked to the size of one "unit" of distance. Any link that you ascribe will be entirely arbitrary.
If 1m*1m*1s is a cube then why isn't 1ft*1ft*1year?
Assigning the speed of light is just as arbitrary, it only applies in this geometry and is not a function of a normal euclidean geometry.
It might just be best to accept that the speed of time is 1 second per second and it is a fourth dimension in the sense that it is a fourth number that you can assign to any point in "spacetime".
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