Hmm that's not quite what I was trying to say when I compared it to Star Wars. The point is connotation. Sure, let's say they do have a choice to translate it as "choose" or "pick". In English, certain words can have the same literal meaning ("Father" or "Dad" being the male parent of a child), but their connotations are different ("Father" is typically more formal, whereas "Dad" is less formal). These nuances that arise from connotations are especially noticed by native speakers. The scene with Beatrice is very emotional. Although to "pick" has a very similar (if not same) literal meaning as "choose," its connotation is one of less focused intention, and more of whim, whereas the latter's is one of more focused intention.
For example, it wouldn't sound right to say "I chose an apple from the tree." Most people don't put much thought into deliberately choosing one apple from a tree (unless your job calls for it, or something). You use "pick" to show a casual intention, and pick in this case can be used to describe the physical act of grabbing the apple.
Similarly, to "pick" a person implies lack of focused intention. This is why many people compare it to a kid playing a game and "picking" their teammates (even if "choose" has the same literal meaning). Therefore, "pick" lessens Subaru's intent for Beatrice to select him as "that person," who she has been waiting for for 400+ years. This selection by Beatrice is obviously not one of casual intent, which is why "pick" is not the appropriate translation.
Of course, not everything is translated perfectly, but this scene is arguably the apex of the entire arc/season. Such a blunder is thus magnified by the community, which understands the importance of this moment.