She didn't need to explain to Picard that the timeline was FUBAR and he needed to send the C back to fix it. Picard is smart enough to figure out for himself that sending the C back might have been a way to alter history for the better, without previous knowledge that an alternate history may have happened.
Based on what? The only reason Picard had any motivation that the C's arrival in the future had FUBARed things was Guinan, and even then it took a lot of convincing to bring him around. He even asks her point blank why he should accept that the alternate history, even if grim, isn't the correct one and why he should make a decision that would almost definitely kill another crew. I don't think Picard or anyone else would have noticed the changes without Guinan's presence, and that's not a criticism of their intelligence. They needed an outsider's perspective to recognize them, because the changes made them incapable of doing so.
Yar is a brave enough woman to volunteer for the probable suicide mission all by herself, without Guinan's mystical "you should be dead" crapola. It would have been a much better character moment for her to say "Yessir, I know I won't be coming back, but I am the right person for this job, period."
Which she does, in a somewhat more meaningful way in my view, because she knows from Guinan that her death can count for something vs. being an empty act of brutality in the proper timeline. That's what gives the "you should be dead" part meaning.