If Bitcoin is fine trading with around 16,000,000 coins, then why does any other coin need more?
But that is what many are missing, 16 million coins means high prices which completely destroy the utility usage for micro-payments.
By having a larger quantity of coins , it allows a coin to be at a much lower price and never lose the micro-payment utility.
Also for Proof of Stake coins, the more coins the safer the network.
Even at less than $600 per BTC, it is unsuitable for micropayments and its transaction fee is high enough , that you are better off using another coin to keep your transfer fees low.
Example:
Now lets look at BTC Utility as a payment system,
To send $4 it costs me almost ~25 cents, and that is with the current BTC ~$600.
With LTC, I can send $4 and it cost less than 1 penny with LTC current price ~$4 per LTC,
LTC price could increase 20X up to $80 per LTC and it would still be cheaper to send as LTC than BTC.
Meaning BTC will not be able to hold on to a Payment System as a utility.
Kiklo is right.
Also the expected use of the coin is important. Bitcoin is an awful currency if you want to buy cheap things like a cup of coffee or a stick of gum. Who wants to count zero's every time they pay?