I think you hit the nail right on the head. A cryptocurrency can only succeed, if there is a limited number of them- ideally, one. How could BTC stop all other cryptocurrencies from achieving any traction?

I think you need to have some authority that limits the number of different cryptocurrencies. BTC has all the momentum right now, but if you're like me, you should be worried about a future with thousands of equal cryptocurrencies, and new ones being created daily. This would go against the very idea of a limited supply, because in such case, the monetary unit wouldn't be BTC any more. It would be "a cryptocoin".

I actually learned about network effects, when I did a paper on iPhone vs BlackBerry at my school.
One thing I remember is that network effects are strong only when a consumer has no reason to have two (or more) of the same items, like in case of a cell phone. Is there something about BTC that would prevent people from using other cryptocurrencies simultaneously?

Not true. The dollar value right now makes me want to buy LTC more than BTC.

Your words perfectly describe what I don't understand after 6+ hours of research. Why is BTC more useful than LTC?

tldr;
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Why is 1 bitcoin currently worth about 100 litecoins?
https://mcxnow.com/exchange/LTC

The longer version
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First of all, let me admit that I may not be thinking rationally right now.
Two years ago, a friend of mine and I decided to stash some of our respective savings away from the effects of QE; he chose Bitcoins, and I chose gold. Needless to say, I am now jealous of him and furious with myself.
Today was the third (and by far longest) time that I researched cryptocurrencies.
In 2011, I spent 10 minutes and dismissed them; this spring, I spent about 1 hour and dismissed them again; but today I've already spent 6 hours and finally agree that cryptocurrencies have a future. So I am ready to buy me some bitcoins- but then I see that there are also litecoins, peercoins, and what not.

How should I choose which crypto-coins to buy? Are merchants going to accept only one crypto-currency in the future? If so, what makes bitcoin better than all others?