I would suggest reasons for why we
(1) We tend to think of the role of a medium as a solitary one. Think of every movie and TV scene involving a visit to a medium. It was always a “singular” experience—as long as one doesn’t count the accomplice in the closet who was pulling the wires and producing the sound effects.
(2) The plural of medium which relates to people is basically already assigned in our brains to journalists et al who constitute the media. Thus, if someone told you that they were going to attend a “media convention”, you’d probably not imagine a bunch of hucksters carrying their mystical crystal globes in what look like bowling ball travel bags. Instead, you would imagine a bunch of hucksters who work for Rupert Murdoch and cable TV channels. [Sorry. Was that too political?]
Of course, the has-been linguist in me will risk offending those who hate etymologies and morpheme studies by pointing out that 2nd declension neuter nouns in Latin end in -um in the nominative singular and -a in the nominate plural. Sometimes our ears rebel (at least a little) when neuter inflections are assigned to people. Yes, a little big of agar in a petri dish constitutes a growth medium but no people are involved so the neuter sounds just fine. But there’s something almost strange about medium and media applied to an animate human. With the singular medium, we’ve grown to accept its assignment to a human thanks to repeated exposure to the concept—but not so much with the plural media (as in plural of fortune-tellers and necromancers.)