Honestly it's a gimmick to cloud the real price and provides little to nothing to the project itself. If projects are promoting it instead of what they are actually doing than it should be a red flag for anyone. It's a smoke and mirrors game, stops people from asking what they are really doing with the project.
Indeed. If the project only focuses on the burning program without developing the project itself, burning won't impact anything. When there is no demand on the market, lowering the number of the tokens will be nothing. But if the project grows constantly and they also have a good trading volume on the market, burning program will be helpful. So, it actually depends on the quality of the project and how the demand on the market.
The rug will come when everyone believes in what is called Burn Token. Even though that doesn't guarantee that the token can be trusted.
Burning never guarantees the quality of the project. It is only the way to lower the number of total supply of the tokens. To know the quality of the project, we need to analyze many things on the project. Check the quality of the developers, how strong the community, how the market caps & daily trading volume, and check the partnerships are some of parts of the project what we need to analyze carefully.