Dividing a unit infinitely (Which is not the case with Bitcoin anyway) doesn't make it unlimited, since it's still the same 1 Bitcoin.
In order for Bitcoin to ever work, it would practically have to be divided infinitely. If it were ever to expand to be the primary currency of the planet and oil and all other commodities were denominated in Bitcoin. If stock prices were quoted in Bitcoin. If derivatives contracts were quoted in Bitcoin. Another obvious flaw in Bitcoin is that no more can be made, but it is possible to loss them permanently. In fact, aren't most Bitcoin's lost permanently upon death of the owner? Even if that's not the case, it's still not good that the supply goes only down. A strong and competent central bank is what keeps a currency stable despite of whatever market conditions are going on around it. Bitcoin is way too volatile for people to ever trust it. There is too much speculation involved. People would constantly be hoarding it or selling it in mass, depending on the outlook.
That's the thing, I don't believe Bitcoin will evolve to be the currency which everyone on the planet uses, not even in a single country. It will NOT become a widely used currency or medium of exchange. It is moving more towards being a very secure & portable Store of Value/Wealth. For that purpose, it doesn't really need to grow in market capitalization that much (To the order of the 100s of trillions). It will only need to grow close to the gold market cap and eventually I believe it will overtake it as well.