I would love to be able to set a "surplus" threshold as part of this solution, say $5k (just an example - it should be set by the user), such that any amount above that in the account is invested, while the rest is kept in cash. That would solve the "emergency" funds issue for some people.
I think framing this is a checking account is what people are having trouble with. It really seems like an investment account with easy liquidity. If you add a section that is kept in cash, then it's checking + investment with automatic rebalancing.