is Bitcoin a pyramid scheme?

My answer is "it's complicated". Honestly, bitcoin is just too different from too many things to really be pegged at the moment.

Also, I propose that we use SI style units for talking about bitcoin in day-to-day life... So right now, with bitcoin trading at $100, a cBTC is worth $1, and a mBTC is worth 10 cents.

Let's look at some of the takes on it:
At the moment, everything that I consider to be a traditional currency derives its value from one or both of two places.

The first, and clearly the elder of the two, is being backed by a valuable commodity. This is less common these days, but you still see it quite a bit... for instance "Sam has 100 pounds worth of gold. This note says that Sam will give you a pound of gold for it at any point" It's a pretty straightforward idea. As long as you trust Sam, and trust the paper, it's as good as gold, better in a lot of ways (like connivence) Sam may have also put out 200 one-lb-notes despite only having 100 lbs of gold. but that can still be ok as long as everyone doesn't want to turn in their note at once. (A side-effect of this is seigniorage [] )

The second, and probably the most related to what we think of as currency now, is that the bank notes are backed by "men with guns". The classic way that this is done is that men with guns, typically a government, demand a Tax be paid to them annually, and that said tax can be paid with one of these slips of paper that says "one dollar". Since most must pay the tax (or suffer violence), the paper that says "one dollar" has been given a real value in that it avoids violence. Even if only some of the population needs to use them to avoid violence, that makes them valuable to everyone.

In practice most modern currencies are a tangled mess of both modes. For instance, the us dollar is backed by currency and gold reserves, but clearly not in anything like enough quantity to support it's value alone. In addition it clearly holds the majority of it's value in that it buys off "men with guns". Even weirder though, most of those currency reserves that it's backed by are also backed by other currency reserves, as well as.... men with guns. Tucked away in there are some big piles of gold and silver to boot.

Bitcoin has neither of these attributes.

What does bitcoin have?

Well, it's first, and probably most productive use, is basically as a modern, high-speed, high-security travelers check (sort of). When the ecosystem is up and running (which probably shouldn't be too long now) it will make a great mechanism for moving money between international parties. You simply buy bitcoin locally, push it to your recipient, and they sell it locally. Acting in this way, you might expect bitcoin to have a total market value similar to visa/mastercard/AMX/paypal and the like. Perhaps a bit higher since it's basically attack-proof. (At the time of this writing bitcoin is nowhere close... it's at $100, and there are ~10 million issued for a total value of ~1 Billion. Visa has a Market Cap of 110 Billion)

Bitcoins second modality is as an secure* storage of value. There are a lot of people who want to tuck money away safely, for various reasons, many of which are illegal. There is a huge value to this service as well. I have no idea how to estimate that. What's better, it interacts well with the first service, providing additional stability of value, and people who want to buy or sell on both ends.

Third, there is the speculation value....
This is the part of Bitcoin that is a pyramid scheme. Because bitcoin has come nowhere near it's stable value (whatever that is) There is a lot of money to be made by "getting in early". Conversely, the total lack of stability that this brings is detrimental to the first two uses. It makes it an insecure place to store money (who want's to stash cash in a volatile place?) and it makes using it for day to day exchange (slightly) more difficult.

Finally, and this is in the very long term...
It may be more destruction-proof than most traditional currencies. As big and unstoppable as they seem, most nation-states only last a few hundred years, and frequently manage to miss-manage their currency out of existence in the interim. Bitcoin is based on participation and math. The math part isn't going to fall apart, and as long as some chunk of the internet keeps running in some chunk of the world, it will likely live on.

further reading:

*secure meaning "cannot be forcibly taken". Value fluctuations are still a huge vulnerability, particularly at the moment.