Doing this makes you retain all the advantages of running your own MTA: none of your emails are hosted at a third party provider, no scanning of your emails to personalize ads, no government agency can knock at the door of an email provider and ask them for the content of your inbox, etc.
The only downside is that in theory Google can scan and block your outgoing emails (not incoming emails since these hit your MTA directly). But if you don't send spam, this should never happen.
Another option is to route your mail through your ISP's MTA. Yes ISPs usually offer SMTP relay service accessible only from their customer's IP addresses (eg. for Comcast it is "smtp.comcast.net" IIRC.) However the reputation factor of an ISP's MTA might be worse than Google's MTA.