Is there a use for Bitcoin (BTC) for savings like a savings account, and Bitcoin Cash (BCH) for daily spending like a checking account?

Individuals can manage their own finances however they wish, and split their "savings" in to Bitcoin and "spending" into Bitcoin Cash if they like. However, in the long run, Bitcoin (BTC) is irrelevant in a world where Bitcoin Cash (BCH) exists, similar to how telegram services became completely unnecessary once telephones were widely available, or landlines with the proliferation of mobile phones. It is even possible to get on-chain price exposure to BTC while holding only non-custodial BCH through AnyHedge, so there is no commercial need to hold expensive-to-transact BTC even to speculate on the markets.

Bitcoin Cash (BCH) can support the entire range of transactions from $0.01 up to millions of dollars at low fees, while BTC can only support a limited range of transactions starting around $100+ due to fees often being $5+. BCH is useful both to spend (any size) and save, while BTC is only useful to spend (moderate - large transactions) and save (moderate - large amounts). Therefore, individuals that balance their accounts between BTC and BCH will increasingly find that they have no need for BTC and transferring back and forward to BCH is an expensive hassle that adds no extra utility compared to just holding and spending everything in BCH.

BCH holders often have separate BCH wallets for their long term savings ("cold storage") and their daily spending though, which achieves the same effect as the bank account. They may use different wallet providers to facilitate this arrangement. The expensive & hassle of replicating this financial arrangement on BTC is one of its many problems.