I agree with EVERYTHING you said and I say more, they MUST fix this fragments system and REDUCE / INCREASE the probability according to rarity.
To be able to acquire common girl it's almost impossible for me to get 6 shards in 20 battles against bosses like Silvanus, Bremen, Finalmecia and Koro Sensei, which is currently my last unlocked world. And I already got the other girls from the worlds that I did not tell.
If for me it is difficult to have these girls, it is worse when speaking of an event, since it has a limited time and the difficulty is the same.