Where are you, fellow enthusiasts?

The problem is that the root cause of the observed facts may be something completely different from what we think. History proves this.

History proves that humans generally don't understand the structure of the world, and all their theories, from the first to the last, are nothing more than attempts to create makeshift solutions to somehow interact with the world. Perhaps clumsily, but with sufficient effectiveness.
Before moving from one makeshift solution to another, it is necessary to ensure that this "other" solution is actually created. If it is not created in advance, and the existing solution is taken away, our "disabled" person will fall and will no longer be able to get up. That's what I'm getting at.

Special and General Relativity may explain a lot, but they also prohibit traveling faster than light. What if they are not correct, but simply mathematically explain the "observed phenomena"?

That's exactly it. However...
But the problem with Special Relativity is that... I personally don't know of any facts that go beyond its scope. Therefore, it is necessary to formulate something truly elegant in order to abandon it, if one really wants to. Perhaps someday we will do this, but for now... For now, it exists, that is.
General Relativity has flaws in the form of dark matter and dark energy. But General Relativity actually allows for travel faster than the speed of light.