Higher yields are possible with various different investments but they all come with additional risk. You do not want to have an emergency fund they may drop in value during a period which you may need to draw on your emergency fund, such as a market downturn that leaves you unemployed.
Similarly, you want to be able to access emergencies funds quickly. Emergencies are generally unexpected. If you need to wait for funds to unlock or for sales to settle, then it could possibly be too late.