If the rules were written for psyker models, everything would be simpler, yes.
Sadly the psychic rules use the terms "psyker" and "psyker unit", which both refers to the exact same thing: "a unit with the Psyker / Brotherhood of psyker rule". So when you say "My psyker is casting this power" what you say is "my unit with the psyker rule is casting this power".
When individual psykers are by themselves everything works fine. But as soon as you get one psyker model in the same unit as other models (psykers or not), everything breaks. So how do we play the psychic phase? Wether you realize it or not, we all play it the same way: we consider that multiple psykers in the same physical unit are in fact different individual psyker units when it come to the psychic phase.
For example, if someone's
GK grand master (psyker lvl2) and
GK librarian (psyker lvl3) join a unit of paladins (brotherhood lvl1), we will all consider them as 3 separate psyker units even though they are forming one single physical unit: each of them will generate it's mastery level of warp charge dices, the perils of the librarian cannot go on the paladins or the grand master, etc.... That's perfectly normal it is the only way where the rules actually make sense. And if you are consistent with how you play, then two psykers in the same physical unit can definitively attempt to cast the same power (provided they both know it of course) during the same psychic phase because you treat them as two distinct psyker units.
So how come some players will still argue the opposite ? Well
IMHO there is two main reasons:
- First some people don't know how to read rules (context? what is that?). They will take a sentence/paragraph, remove half of it and throw it to your face saying "booya you're wrong, my truncated text with ultra-
RAW reading wins". And they will not realize how inconsistent they are in their reasonning.
- But the more probable reason has nothig to do with rules. When 7th ed came up, the SeerStar and the ScreamStar were top-tier armies and as such the target of a lot of hate. At the same time Invisibility changed and became gross while summoning was the new
40k boogeyman. Other powers were of concern too, but those were the big ones. Guess who could spam those powers ? The SeerStars and ScreamStars! So yeah, when you add the cheesiness of those armies with the fear (justified in some case, not so much in others) of those new powers, then you quickly understand why a lot of people decided (or voted) to just prohibit multiple cast of the same power within the same unit.
TL;DR: Two psykers in a unit can't cast the same power not because of how we understand the rules and actually play them, but because of balancing issues and fears of now bygone days.