Now, on logistical level, the mapping procedure is not free, it does have a physical/energetic/mental cost to handle it, and a more trivial representation of integer has a lower cost on this regard.
But the simpler integer representation can represent less many situations. If all one need to deal with in a certain frame is covered by a simpler shipper representation, from an economical perspective it can be argued it worth the risk of hitting a point where the representation will be insufficient as the situation evolved with cases it can't handle.
My impression is that your underlying premises are conflating all of this distinguishable aspects. But of course my impression is limited by my own narrow representation of the world, no matter how open and curious I can be about learning from experiences it makes me go through.
I sometimes wonder how much we allow the map to become the territory.
That said, I accept that literally, 3 never occurs between the ∞ of 0-1 -- unless, we are assuming symbolically, rather than actual, that in our particular ∞, something does not transcend entirely, which we really cannot know, because the closest we have ever come to a real infinity is a representation or symbol of it.
Edit: I realized that the question appears, or is, stupid. But when I see 0.3, I tend to see the 0.0, 0.1, 0.2 between. This is not what 0.3 is supposed to mean though. But on the testability of any real infinity, I do not budge.