My novice understanding of BTC is that BTC is valuable because it's scarce - mathematically, there can only be 21M BTC, no more.
What's stopping another altcoins from starting with the same protocol, but a new chain, rendering the limit of BTC to N * 21MBTC?
Nothing stops this at all. You can start your own right now, removing the 21M limit or adopting whatever rules you want, and mine as many coins as you like.
Likewise, you can sit down at your printer, and print lots of $100 bills with your own portrait, and invent whatever rules you want as to how they can be spent.
The question in both cases is whether anyone besides you will want to use them, and be willing to exchange them for goods or services. You'd have to convince people to use them, that your rules are such an improvement over the existing ones that they should switch. If they don't, then your new coins or bills have no real value.
So there's nothing stopping an infinite variety of altcoins from appearing; but probably only a few of them will be adopted by anyone.
Technically, there is nothing that stops this. There are already dozens of alt-coins that have popped up out there. Litecoin, for example, is essentially Bitcoin with a few tweaks, one of which is a larger ceiling on how many coins can be minted.
Note though that these alt-coins can only exist parallel to Bitcoin, even if they use the same protocol. The only way that Bitcoins are ever generated is when a new block is added to the blockchain, and Bitcoins are never destroyed. You can loose access to coins by forgetting or loosing the private keys in your wallet, but those coins still exist even if they can't be used. Whenever you spend or receive Bitcoins, those coins are simply being moved around within the blockchain like they might be in an accountant's ledger. Bitcoins do not leave the system, and they cannot be introduced to the system from another blockchain, even if it uses the same protocol.
Because the different coins are not inter-operable, what stops too many competitors from becoming widely used is momentum within the market. Bitcoin has a great many people who have invested time and money into it, and they are unlikely to just switch over to another coin at the drop of the hat.
https://en.wikipedia.org/wiki/Stamp_collecting
Looks like something similar to nowadays events with alt-coins already were in the history of humanity.
What can stop Stamp collectors from creating new stamp? Theoretically, there is finite lumber on the Earth, finely, finite number of the atoms around Sun.
Compare to alt-coins, there is finite number of tcp ports, 1-65535. However, any alt-coin can take original bitcoin's ports.
Finite number of IP addresses, however, there is IRC protocol in the base of bitcoin protocol, probably, only one node needs in real IP, may be no one.
An Enter to the market for new alt-coin appear more and more friendly. Probably, once, user would chose couple of params, Number of coins, delays, ports, name of alt-coin, and Logo. Push the button. Alt-coin ready. User will only configure his GPU/CPU to make the life in the block-chain.
