You are missing a very critical point: either you need to rent a virtual or real server and spend time configuring and maintaining it - or you could try and dare to run your mail server from at home on some linux box which will open a whole can of worms...
So gmail gives you an easy and free alternative and you can just sign up and access mail via web, pop3 and especially IMAP, which made it superior to pretty much every single other webmail when they launched that feature - and I believe that is still true today, most free webmail providers don't give you free IMAP. You are "paying" by giving away your private information but evidently, people prefer it to setting up their own mail servers.
So gmail gives you an easy and free alternative and you can just sign up and access mail via web, pop3 and especially IMAP, which made it superior to pretty much every single other webmail when they launched that feature - and I believe that is still true today, most free webmail providers don't give you free IMAP. You are "paying" by giving away your private information but evidently, people prefer it to setting up their own mail servers.