Yes indeed I do use it... It looks more professional to provide an email address based on the domain. The way I do it is to use an email forwarder so that all email's received from my many websites are consolidated into one place under a gmail account. When replying I'll log into the email account so that the reply address is that of the domain and not forwarder....
Same as you guys, I use webmail when replying to an email but every email I receive is forwarded to one gmail account from different emails and websites.
It can be inconvenient sometimes using the *webmail* software cPanel has to offer, however, the server supports imap and pop3 so by creating an email account it is accessible from software such as Thunderbird or even on your mobile device.