I think the intuition that the electromagnetic worldview plays some role here does contain an element of truth. I suggest that the differentiating factor was not Poincaré’s commitment to the electromagnetic world-picture itself, but to the explanatory strategy associated with it. Although he was willing to accept the existence of particles which are not charged and forces which are not electromagnetic in nature, he remained faithful to the underlying motivation for the electromagnetic picture, which is that all observable phenomena should be be accounted for by appeal to the nature of the fundamental particles and forces. This idea was certainly not unique to proponents of the electromagnetic worldview; a similar motivation lies behind the mechanical world-picture, upon which all macroscopic phenomena are produced by Newtonian interactions between moving microscopic particles. ...She is crediting Einstein for ignoring empirical evidence, and for failing to give a mechanical explanation. She admits that Einstein did not say these things, and even implied that he disagreed with them. Nevertheless it underlies the reasoning for crediting Einstein for relativity, and for revolutionizing physics.
It is therefore not surprising that Poincaré never thought to view the relativity principle as explanatory in and of itself; as Katzir puts it: ‘instead of deducing consequences from (the relativity principle), he used it mainly to confirm or refute various hypotheses.’ Poincaré regarded the principle rather like a general summary of the empirical evidence, such that that theories which violated it could be taken to have been indirectly disconfirmed. ...
Einstein’s 1905 paper was revolutionary precisely because he broke with the long-standing tradition of explaining the macroscopic in terms of the microscopic. Rather than taking force laws as fundamental, he made the relativity principle the basic axiom of his theory and used it to derive constraints on the form of the laws governing phenomena at both the microscopic and macroscopic levels.
The interesting point is why Poincaré thinks it is important for P to form a group. In a reconstruction of the proof, Zahar writes ‘In view of the relativity principle, all allowable frames are equivalent, which entails that P must form a group.’ (1981, p. 191) This is the appropriate modern justification for the group requirement, but it is not clear that it is a correct description of Poincaré’s thought process, since he never mentions the relativity principle in the course of his derivation. Of course, he might have thought its relevance was so obvious that the link did not need to be made explicit, but this seems unlikely in view of his understanding of the Lorentz transformations.Yes, the importance of symmetries forming a group was obvious to Poincare. He called it the Lorentz group in a short relativity paper that Einstein had access to before he submitted his own 1905 relativity paper. But Einstein himself did not seem to understand the importance of the Lorentz transformations forming a group.
Einstein, on the other hand, is much more willing to discard conventions - perhaps the clearest example is his willingness to adopt a new synchrony convention which violated traditional ideas about the nature of time. Poincaré would theoretically have agreed with Einstein that simultaneity is determined by a synchrony convention, but unlike Einstein he always retained the traditional conventions in his scientific work.She refers to Poincaré–Einstein synchronisation, which, as Wikipedia notes, was published by Poincare in 1898, 1900, and 1904, before Einstein first wrote about it in 1905.
The problem with these Einstein scholars is that they fail to address the basic facts -- that Poincare had the Lorentz group, the synchronization, the spacetime, the mechanics, and everything else years ahead of Einstein. The only way to credit Einstein is to invent some interpretation of his paper that is contrary to what Einstein believed and contrary to modern physics, and brag that it somehow distinguished Einstein from Poincare.
When physicists promote goofy ideas like string theory and multiverse, they always claim to be following Einstein's example of revolutionizing physics by postulating principles and ignoring evidence. I detail this in my book.