An invoice from ahmed.design.2019@gmail.com and one from accounts@yourbusiness.com might ask for the same amount, but they don't inspire the same confidence. Clients notice, and so do spam filters: a properly set-up domain is far more likely to land in the inbox than a free address sending business mail.
The bigger cost of a messy setup only shows up later. When the person who handled a client leaves, their personal inbox leaves with them, and so does the history of every quote, approval, and complaint. We've seen businesses lose months of correspondence this way. Email on your own domain belongs to the business, not to whoever happened to be using it.

