That isn't a flaw as that doesn't apply to everyone. Plenty of people focus 1 or 2 teams over the rest and as I said, put more effort into 1 team while slowly working on the rest. It doesn't mean you only play that 1 team forever.
Cores can eventually be used for awakening as well as trading in for draconic eyes shards which can be used for SR guarantee hime weapon ticket and SSR tickets. More stuff will be added in the future such as many of the non hime SSR weapons in the gacha into the exchange shop (don't forget gacha weapons are by far stronger than any event weapon) and I believe items that can be used to break limit any SSR eidolon/weapon.