I have a couple sites I have hosted and email servers come with them. So if you want to call that "your own", it's pretty easy. Not free, by any means but you have full control and can make email addresses all day long. Want to enter into a contest but you're pretty sure it's a spam list? Make an address just for that, delete it when you're done. And so on.
As for your own physical email server, you need a box, a domain of your choic... you know, here's a tutorial on how to do it with a raspberry pi (dirt cheap and almost no power usage): https://samhobbs.co.uk/raspberry-pi-email-server
So a raspberry pi is a one time $35 (or cheaper) and the domain name is like $12 a year. If you want SSL, you gotta pay for that.
But to answer your question directly: extremely practical. There's no reason why you can't if you have any inkling of doing so.
Thanks for the info. I read an article a while back about a guy setting it up all from scratch (so not automatically included with your site), and he was saying his mail would get flagged as spam when sent to gmail, yahoo addresses, etc. So maybe the situation is better when the email is provided by your webhost.
You have to have your headers, reverse dns, etc ad naseum correct and even then you have to not have your domain listed in a spam clearinghouse or all the major free email providers will shuffle your emails into the junk folder.
Setting it up from scratch isn't as easy as just flipping a switch, opening a port, and sending.
How practical is it to run your own email server? Is spam a huge issue? Do your sent emails get labeled as spam by other services?