Plenty of real companies run on a free mailbox, and for a while nothing goes wrong. The problem is not that a free address looks unprofessional, although it does. The problem is that it belongs to somebody else, and every consequence of that arrives at once, on a day you did not choose.
The address is an asset, and only one version of it is yours
An address on your own domain is something you own. If you change provider, you take it with you. Your customers keep writing to the same place, your invoices keep quoting the same contact, and nothing on the printed material becomes wrong.
A free address is a licence, not property. You cannot move it, you cannot take it with you, and if it is ever suspended for a reason you did not cause, there is no support desk that treats it as a business matter, because commercially it is not one.
It changes whether people trust the message
A quote from sales@yourcompany.ge and the same quote from yourcompany2019@a-free-provider.com are read differently, and the second one is read with suspicion by exactly the people you most want to convince - finance departments, procurement, anyone who has been trained to look at the sender.
It matters in the other direction too. When a customer receives a message that appears to be from you, the domain is the only part of the address a forger cannot casually reproduce once it is properly configured.
It survives people leaving
Every business eventually needs to answer a mundane question: an employee has gone, and their conversations with customers went with them. On your own domain that is an administrative task - reassign the mailbox, forward it, keep the history.
When the address belonged to the person rather than the company, there is no administrative answer at all. Whoever knows the password owns the customer relationship, and that is a bad arrangement even when everyone involved is entirely honest.
What it actually takes
Less than people expect. You need a domain, a mail service, and a handful of DNS records that tell the rest of the world where your mail lives and who is allowed to send as you.
If your domain uses our nameservers, the records can be set up for you in a single step from your account, correctly, including the ones that stop your messages landing in spam. If it is elsewhere, we will give you the exact records to paste, and check them afterwards.
Start with the addresses that matter - the one on your invoices, the one on your website, the one your team actually uses - and add the rest later. There is no requirement to move everything on the first day.
One thing to do properly from the start
Set up the sender records (SPF, DKIM and DMARC) at the same time as the mailbox, not later. Without them, mail from a brand-new domain is treated with suspicion by every large provider, and anyone can send messages that claim to be from you.
They are three DNS records and an afternoon of attention, and they are the difference between mail that arrives and mail that quietly does not. There is a separate article here explaining what each one does.