But you just encrypt something with it and ask Alice to decrypt it with her private key and you ask her if she was able to.

Oh god but how do you ask her without a guarantee that she's really who said yes?

Even if you meet Alice in real life to ask, how can you be sure the meeting isn't a dream or a simulation and the Alice before your eyes isn't a chosen plaintext attack by a cosmic man in the middle?!

The entire science of cybersecurity is bankrupt and founded upon untenable foundations!!