With anycast, it would be possible to have the same IP address at multiple locations in the world, without the need of a proxy or VPN that forwards the packets to its final destination.
If you would just use IP spoofing to change the source IP address to for example 18.104.22.168, normally you would not be able to just receive the response packets for this IP address, as the Border Gateway Protocol determines a different path back for the response packet that you normally won't be able to intercept.
What does anycast do so you can reliably receive IP packets meant for this particular IP address? Since the shortest paths BGP relies on can change, which mechanism ensures that when you send a request at location C that has IP address 22.214.171.124, you will receive the entire response back to location C and you won't receive a response with also a few packets delivered at location A that has IP address 126.96.36.199 and another few packets delivered at location B that also has IP address 188.8.131.52?
For DNS it might not matter, but Anycast is also used by CloudFlare for the content delivery network, which would be HTTP(S) over TCP and not just UDP Packets.
How about this scenario: Server A and B have the same IP address with anycast. Server B connects to an external server that is very close to server A and very far away from server B, since server A is closer, the response will be routed back to server A, isn't it possible to always route this type of requests back to server B, since server B initiated the connection to the external server?