In a lot of these types of games, the pick a card thing is just an animation and your reward is already predetermined behind the scenes. Since it's digital and not an actual physical card you're flipping, it makes more sense to do it this way since even if the card you picked did matter, it would be the same as giving you a random card, since there is no element of skill involved (it's not like you can try to follow the cards being shuffled to try and pick the one you want). I'm pretty sure the survival breakthrough cards work the same way as well (predetermined rewards in order of flip, so no matter which cards you pick the rewards will be the same for each pick).

Now I don't know if this is how it works, but I'd expect it is because it would be a lot more (unnecessary) work to make your choice actually matter vs giving you a random drop. The card thing is probably to motivate players ("look at what else you COULD win"), but like you said it probably just makes most people salty. I just ignore the other stuff now when I get my rewards to avoid getting frustrated.

If I had to speculate (for TI), it would be pull random stuff 5 times, assign you the first one, and then randomly display them.

I agree that it's a bit shady, but both of these features are free things that players do anyway, so even if they're showing you rewards you can't get, you're still going to do survival breakthrough. If they did this card picking thing with something you had to actually pay for, that would be a much bigger problem. It would be nice to know how it works, but I'm not holding my breath lol.