The solution is simple. Use the gold model. Only allow whole bitcoins to be sold. Precious metal markets sort of work this way. Sure you can buy gold by the gram, but you pay a lot more so it's not something you do frequently. Gold is best bought by the Troy Ounce at a minimum. Bitcoin can also be sold in fractions, but there should be a premium to do so. This will reduce the day trading that causes the huge fluctuations that makes it feel like Bitcoin is not increasing in value. Buying a whole Bitcoin may also become an exclusive goal for the rich and attract them faster. This way, fractional amounts will not be worth gambling on the markets.
This is of course only a thought experiment and impossible to implement without strict government regulation anyway. However, it behooves the exchanges to consider this proposal because it would likely serve to increase transactional revenue as Bitcoin will have less volatility and greater appeal to conservative investors.
This will also incentivise vendors to accept Bitcoin because they will accrue fractional amounts without paying a premium and can sell them at a premium.
You think we should kill one of the biggest advantages bitcoin has over gold?
+1
Actually doing what OP suggests makes bitcoin equally worthless as a currency as gold.
If OP wants to solve Zeno's Paradox I would suggest using a different measure like millibits or satoshi, just to mindfuck people.
That said, volatility attracts traders and trading evolves a market and brings it to maturity. As the price goes up and bitcoin adoption increases volatility will be suppressed anyway...