The problem the handshake solves
WPA2-Personal protects a network with a shared passphrase, but sending that passphrase over the air — even once, even hashed — would hand attackers everything they need. The 4-way handshake solves a harder problem: both sides must prove to each other that they know the same secret, derive fresh encryption keys for this session only, and switch encryption on at exactly the same moment, all over an untrusted radio channel.
Before the handshake begins, the device and the access point have already found each other (probe), exchanged a legacy greeting (Open System Authentication, which checks nothing), and associated. At that point the client is attached but quarantined: the IEEE 802.1X controlled port discards every data frame. No password proof, no traffic.