Not a big one if you e.g. have someone else provide the backing email service.
I bought my own domain back in 2002 or so, and note it's important that you own it*, and then set up email with a quality shared hosting service company. At some point I noticed this well recommended Fastmail company, which was lots cheaper than the shared hosting, the other features of which I no longer needed. Which has now been providing my email service for years, and I note they also do contacts and calendaring. And have really good customer service. And are reliable, including not having GMail's sometimes too aggressive spam filtering. Etc.
Although if I remember correctly they were pants at accepting notifications from Fanfiction.net, which is not something I really worked at fixing since it prompts me to regularly check my backup Hotmail (Live, whatever) account. Which emphasizes one thing, if you do this, make very sure to maintain another email account in case you have any problems with your personal domain.
You also ought to get treated more seriously by various important others if you have your own domain instead of a generic GMail or other big free email provider account.