E-mail is one example. Technically domain names are not necessary to successfully send own mail with own server, i.e., without using a 3rd party email provider. E-mail predates DNS; mail software has always supported IP addresses. However, today, the dominant 3rd party e-mail providers will reject mail coming from an IP address not associated with a domain name.
The patchwork of anti-phishing and anti-spamming measures like SPF and DKIM require DNS TXT records. Allowing mail from an IP address would likely be used almost exclusively for spamming.
E-mail is one example. Technically domain names are not necessary to successfully send own mail with own server, i.e., without using a 3rd party email provider. E-mail predates DNS; mail software has always supported IP addresses. However, today, the dominant 3rd party e-mail providers will reject mail coming from an IP address not associated with a domain name.