Today it is easy to create zone files from free, publicly available internet scan data, e.g., scans.io and censys.io. This is arguably a better solution than zone files. Not every domain name in a zone file necesarily corresponds to a website. Whereas scans allow to focus only on websites.
Requesting zone files from the registry was the traditional method. ICANN tries to require registries to provide them to the public, with limited success. Downloading com.zone/net.zone from Verisign should be relatively straightforward (not sure if edu.zone is available anymore). However with gTLDs there are hundreds of registries now, with potentially hundreds of different rules on zone file access; some registries like ccTLDs never had zone file access programs. Even registries that seem like they would be easy to deal with can have silly restrictions, e.g., the .org registry used to have a requirement that the requester needed to have stable IP address.
You can request a copy from ICANN through the Centralized Zone Data Service (CZDS). It's a pretty neat service and will give you access to zone files for a few months, you just need to file a request to one/multiple TLDs you are interested in seeing.
Sometimes larger TLDs take a bit longer to respond to requests, whereas some others automatically accept all requests.
Requesting zone files from the registry was the traditional method. ICANN tries to require registries to provide them to the public, with limited success. Downloading com.zone/net.zone from Verisign should be relatively straightforward (not sure if edu.zone is available anymore). However with gTLDs there are hundreds of registries now, with potentially hundreds of different rules on zone file access; some registries like ccTLDs never had zone file access programs. Even registries that seem like they would be easy to deal with can have silly restrictions, e.g., the .org registry used to have a requirement that the requester needed to have stable IP address.