People forget that Maxwell's Theory contradicts the prevailing belief of the time that waves ALWAYS require a medium for propagation--the so called "aether".
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.
Maxwell saying that his theory "attributes electric action to tensions and pressures in an all-pervading medium... the medium being identical with that in which light is supposed to be propagated" suggests that Maxwell himself did not view his theory to be contradicting the existence of an aether (or was being coy about it). Which is especially interesting because Maxwell based his theory on Faraday's, and Faraday didn't believe in the aether.[1]
[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)
I mean, language is hard, and it evolves. What they called mediums, we now call (quantized) fields. QED would say the photon field _exists_ at all points in space and that it is kinda fair to say that it is a "medium" for electromagnetic forces and waves to propagate (with the additional point that special relativity is required to understand how to correctly transform it into a different reference frame, rather than imagining it as a strictly Newtonian medium).
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.