A business email is important for a few reasons:
- Shows you took the time to invest in and are serious about your business 
- Exudes a professional presence to your clients, potential clients and potential lenders/creditors. 
 
Other reasons a business email is important are: 
It is a lender requirement, for some,  to approve you for funds. 
D&B will deny you a duns number if you have a yahoo, gmail, etc.