Fiat money also have a kind of a hard cap - inflation starts if there are too much pieces of paper (or plastic) that are not supported by precious metals, goods or servies.
Remember what happened to Zimbabwe? Inflation there has reached some crazy several million percent over the past years.
Still the whole world uses paper money without thinking of some "hard caps" because they regulated it in a certain way that allows all these "cents", "centimes", "kopecks" and so on.

In this way, satoshis will rule when all BTC are mined.
Let's do the simpliest calculations:
1. 21 million BTC * 100 million satoshi = 2,100,000,000,000,000 (2 QUADRILLION) satoshi .
2. Divide 2,100,000,000,000,00 satoshi to 10 billion people that might live on the Earth in like 5 years = 210,000 satoshi per person.
It means that everyone (including old men and infants - and perhaps their pets   ) can get their share of the overall quantity of bitcoins mined.