Why don’t SMTP servers just require all senders to be authenticated before accepting mail?
Laziness mostly. Ease of configuration, it's easier for administrators to setup a central SMTP server which doesn't require authentication to send email, than one that does.
You will often see that this is also offered by ISPs to accomodate their clients more easily.
I believe you are making the following assumption:
This is only half the story.
For example, not many things prevent Trudy from connecting to a mail-provider-a SMTP server and sending an e-mail to email@example.com while listing firstname.lastname@example.org as the sender. mail-provider-a has no way to verify mail-provider-b users. This is not a misconfiguration, this is how the e-mail works.
SPF records can be used in order to verify remote SMTP servers and mitigate the above attack, by making sure the sender's IP address matches the IP address specified in the SPF record for the domain that is being claimed as the e-mail origin. This is not enforced being enforced by many email providers.
This is the reason that people should use e-mail signatures.