Custom Laravel 7 email verification with Twilio Verify and SendGrid allows users to register without verifying their email addresses, decreasing the likelihood of being able to contact them again. Email verification exists to correct this user experience flaw, allowing users to sign up and receive a secure token sent to their email to confirm that they're both real and have provided the correct email address. By adding verification logic in Twilio Verify and SendGrid, developers can override Laravel's default logic and create a custom solution for verifying users via their email addresses. The tutorial covers setting up a dynamic template in SendGrid, creating a Twilio Verification service, and overriding the MustVerifyEmail contract to send emails using Twilio's credentials, ultimately creating a secure email verification process that replaces Laravel's default logic.