I'm not sure if this is the point you were making, but divisibility doesn't make something less scarce, any more than being able to cut a gold brick into nuggets means gold isn't scarce. A single Bitcoin remains exactly as scarce regardless of how it is divided.
I don't think scarcity necessarily correlates directly to value. Land values are a good example. New land is not getting created, you can subdivide it down to small pieces, yet it's worth more in some areas.
Since Bitcoin is divisible down to a small fraction, and you can trade it for whatever price you'd like, it makes more sense to me for the two parties involved in a Bitcoin transaction to take some tiny fraction of a coin and use that as a token to transfer the value from one party to another. You'd convert fiat -> BTC fraction -> fiat almost immediately.
You would have the benefit of the decentralized network to make completing the transaction much easier, and by using a fraction of a coin you'd remove risk caused by exposure to fluctuations in the value of a whole BTC.