To try to answer that, we first need to figure out what exactly Trump Card is.Not that it matters now that it's been cut, but is there any rationale for the Pokemon that get Trump Card? Eevee, Slowking, Minun, and... Magearna.
There's not a wholly obvious link between those four. Nor what makes Slowbro and Plusle ineligible to learn the move.
Then there's the Pokemon who get it by breeding. Farfetch'd, Kangaskhan, Dunsparce, Corphish, Shellos, Oshawott. Another diverse and relatively unconnected list.
So Trump Card is a quirky sort of move, a gimmick. No other attack works on the basis of its own PP, but like a couple of other Normal moves such as Facade and Endeavour, it works best in a pinch.
Farfetch'd is (was?) a gimmicky sort of Pokemon, as are Dunsparce and Minun, so those fit the move to a degree. Corphish, Shellos, and Oshawatt are all kind of quirky. Kangaskhan learns Reversal and, like a lot of protective mothers in the wild, attacks more fiercely when it's enraged and desperate.
Anyone care to weigh in on the others?
Mechanically, Trump Card seems to be something of a counterpart to Last Resort. Both were introduced in Gen 4, both have names that suggest that they're ultimate techniques that get saved for late in the game when you need them most (fun fact: Last Resort in Japan is called "The Best", as in "saving the best for last"). Additionally, Last Resort is the move that Plusle learns at level 40 instead of Trump Card.
In terms of physicality, Trump Card seems to literally involve attacking with playing cards, judging by its in-game animation and depiction in the show. However, since almost none of the Pokemon seem capable of throwing cards, let alone even be associated with cards, we can assume these are magic energy cards that just get summoned. This doesn't appear to be relevant in this slightest.
This hasn't brought me any closer to figuring out why this random handful of Pokemon learns Trump Card, and just leaves me with more questions.