Standing to the left of the blade, as you should
That is a bit of a circuitous argument.
You stand to the left precisely because the fence is on the right in order that you can see what is going on.
If the fence is on the left, you stand on the right so you can see what is going on.
Starting with a saw and no fence, there is nothing that tells you in advance which side you should stand. At that point it is entirely neutral. It is only when you install the fence that the 'should' powers up.
Contrast this to a chainsaw, where the physical layout of the machine means your body should be to the left of the bar from the getgo. Approaching one of those machines, there is no neutrality.
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I am not sure there is any reason for it being so. It is just one of those things that has developed over time. The layout and controls of the machine have evolved to suit the traditional layout (how many sliding table saws do you see with the sliding table on the right?).
Maybe one small thing to consider is that if you move the fence to the left, and stand to the right, is the big red button still equally accessible when needed? If you need to move across the line of the blade to reach it, that might not be desirable.