Core Question

We've been taught from the earliest of days that a token burn will have an increase in price because it reduces the supply of a fixed cap crypto. However, that is almost always never the reason behind the price increase, at least not directly.

What a token burn actually is.

When people talk about a crypto project burning tokens or an individual burning tokens, what they really mean is that the entity sent a large scale amount of crypto to a burn address. A burn address is just an address that can't have a corresponding private key and thus no one can access the funds, locking them away. 

There is different kind of token burn, and that is a protocol/network physically (well not physically, more like digitally but still) destroying the tokens. The most famous would be any sort of pegged token (USDC, USDT, PAXG, DAI and many more) being destroyed upon return of the associated value or the SOL fee burn, where half of the base 5,000 lamports  fee (so 2500 lamports) are burned per transaction. These are permanently destroyed never to be seen again.

Understanding where burns come from

When a new crypto project or memecoin announces say a 1 million token burn out of a 100 million max supply, investors get hyped, because they think, "Oh wow, that asset is now 1% rarer!" In fact, in most cases, the big amounts you see burned are actually not part of the circulating supply but rather a held back reserve for treasury, ecosystem incentives, rewards, to get some of their own crypto for themselves, or setting up liquidity across DEXs and other exchanges. 

So in our 1 million token burn example, that price could be 10 cents ($0.10) per token. However, there are only 50 million tokens actually released, while the other 50 million are locked away. So when the developers of those tokens announce that 1 million burn, it is coming from their reserved 50 million (nobody would buy $100,000 worth of crypto just to never see it again). 

Once that burn has been executed, the market is dealing with the same amount of the tokens (50 million). So, nothing really happens to the market price. The only thing that would happen would be hype causing extreme volatility. 

Now, there is a real burn that does put some price pressure on the long term that people do, although on a much smaller scale. And that is sending crypto from the circulating supply to burn addresses to make the remaining supply slightly scarcer. One prominent example from May of this year is the 107 BTC sent to the burn address 1111111111111111111114oLvT2 by someone unknown. 

Isn't hype sort of a price increase?

In a sense, yes, but it is very very volatile. Anytime investors or even people who don't know too much about crypto see headlines like "XXX just burned 10%!" or "YYY is now 5% rarer, will it spike?" and a bunch of other headlines, people buy out of FOMO (Fear Of Missing Out), causing a huge price spike even though there is absolutely no change to the underlying asset supply. Once people sort of regain their sense and rationality, they sell, causing the price to plummet, and it can even be lower than the original price before the burn since holders before the spike get out of the token entirely by selling their entire positions.

Final Word

Token burns don't cause a price increase on their own, but rather the hype of investors is what causes the price increase, as the underlying token didn't really get rarer, or at least not rarer for the public. 

Of course, if someone burns BTC, then that will put some upward pressure over the long term, but rarely short term.