It took a lot of careful and detailed measurement to prove that the speed of light doesn't change. But it also took one important thought experiment. The de Sitter Effect showed us how stars would look if light didn't have a speed limit.

Light travels so fast that it takes extensive experimentation before anyone can understand that it actually travels, instead of appearing instantaneously. It takes yet more experimentation to find out about how fast it travels. After that, it generally takes yet more experimentation and debate to settle on the least believable part of light - the fact that it always travels at the same speed regardless of how fast the object making the light is moving. The absolute limit of 186,000 miles per second for light was considered absurd by many. It's still a strange concept. If someone throws a baseball to you at ten miles per hour, while standing on a moving sidewalk that is also moving at ten miles per hour towards you, you'd expect the ball to hit at twenty miles per hour, and you'd be right. Given how fast objects in space move, the speed limit of light would be like having someone sit on the wing of a jet coming at you at seven hundred miles per hour, and throwing you a baseball which hits you at twenty miles per hour because that's just how fast baseballs move.

In the early 1900s, people were having exactly this debate. Those who argued for a constant speed of light, no matter how fast the objects that emitted or received the light moved with respect to each other, had evidence on their side. No one had managed to get a glimpse of light (in a vacuum at least) moving at any different speed.