The default MX records cannot be deleted but it does not affect how you will receive your emails with GoDaddy, you will be able to receive your emails just fine.
I don’t have any experience with GoDaddy and their services but I don’t know about this "smtp.secureserver.net" if these are supposed to be an MX record which is a DNS record or an SMTP, SMTP and MX are different, SMTP is a protocol or a way to send your emails to another email address and MX records is used to specify the mail server in charge of accepting incoming emails.
If you have not received the emails by using GoDaddy’s MX record then try asking their support to get correct MX records that you will have to add here. Also take note that it takes up to 24 hours until your DNS records will be propagated so you cannot receive emails immediately if you’ve just recently added your MX records.
Also please refer to this Knowledge Base article: