They do - well sort of.

The most essential check is SPF and DKIM which authenticate if the message has come from an authorized server. The problem is that most mail services are too lenient with mismatched sender identification. On one hand, people would be quite vocal about their mail provider sending way too much legitimate (but slightly misconfigured) mail to the spam folder. However it allows situations like to happen where the FROM header, the "From:" address, and the return path are all different.

Most mail systems have several stages of filters, and the first ones (checking authentication) are quite basic. After that, attachments, links, and contents are checked for known malware. Machine learning might kick in after this, if certain criteria are met. Mail security is very complicated and works well except for the times it falls flat on its face like this.

https://en.wikipedia.org/wiki/Sender_Policy_Framework https://en.wikipedia.org/wiki/DomainKeys_Identified_Mail