That's a really large conceptual jump and physicists did not make that jump lightly or easily.
Maxwell's paper was 1865. The Michelson–Morley experiment was 1887. Michelson himself couldn't make the shift. Quoting Wikipedia (https://en.wikipedia.org/wiki/Michelson%E2%80%93Morley_exper...): "The negative result led Michelson to the conclusion that there is no measurable aether drift.[1] However, he never accepted this on a personal level, and the negative result haunted him for the rest of his life (Source; The Mechanical Universe, episode 41[8])."
In an attempt to preserve "aether", Lorentz contraction then enters the picture as an ad hoc explanation for the Michelson-Morley result. It turns out Lorentz contraction is correct, but not because of the existence of "aether" but because of the constancy of the speed of light--c (Einstein Special Relativity--1905).
Once you finally give up on "aether" after 40 years of trying otherwise, you can finally just roll with the mathematical implications of Maxwell's equations.
[1] Michael Faraday's Thoughts on Ray Vibrations, 1846, cited by Maxwell in his paper. Faraday says: "The view which I am so bold to put forth considers, therefore, radiation as a kind of species of vibration in the lines of force which are known to connect particles and also masses of matter together. It endeavors to dismiss the aether, but not the vibration." (https://pwg.gsfc.nasa.gov/Education/wfarad1846.html)
We did get stuck with Gibbs' vector calculus formulation as the canonical view unfortunately.