It's important to remember that the main thing Bitcoin needs to maintain is it's monetary policy and you can find it at any time right here https://github.com/bitcoin/bitcoin/blob/master/src/validatio... Anyone can query at any time the total amount of Bitcoin that have been issued without relying on anyone. After downloading the Bitcoin client just run gettxoutsetinfo You can try to guess how many dollars have been…
No-one in their day-to-day usage of dollars (or gold) directly cares how many currency units exist. What they care about - and what is very easy to know, is what the purchasing power of their currency is.