Digital signatures solve the problem of sender impersonation (at least technically) end-to-end:
A digital signature is a mathematical scheme for demonstrating the
authenticity of a digital message or document. A valid digital
signature gives a recipient reason to believe that the message was
created by a known sender, such that the sender cannot deny having
sent the message (authentication and non-repudiation) and that the
message was not altered in transit (integrity). Digital signatures are
commonly used for software distribution, financial transactions, and
in other cases where it is important to detect forgery or tampering
Signatures can be used in email through S/MIME and PGP / GnuPg certificates. For example Thunderbid has a popular Enigmail extension interfacing with GnuPG to check and sign messages. Outlook supports S/MIME.
To sign a message, a sender uses a private key that must not be shared. To check a message, a receiver uses the public key of the sender, which can be shared to everyone interested in validating this sender's messages.
Such public keys are available through key servers. There are also key signing parties in which people physically meet to assert that they are who they pretend to be and sign each other's digital certificates.
So it's not that no one thought about the problem, actually it was studied in detail, solutions are implemented and have been available for a while, including in free software.
To me the question would be: Why isn't everyone using that already? Why aren't large mail providers like GMail or Outlook.com or Yahoo Mail proposing digital certificates along with email accounts, encouraging and helping their users to sign their messages?
Why when joining a new company, an employee generally gets an email address and a password to send/receive messages, but not a pair of digital keys to properly sign his/her messages?
Probably, we're collectively too complacent or lazy to take the necessary steps. Maybe it's like switching from IPv4 to IPv6. We know we should do it, but we're scared of the change and effort and wait for the rest of the world to do it first, and it doesn't happen.