Slightly OT question, but why wouldn't this be a problem with ingress, too?
E.g. suppose I want to send a request to https://1.2.3.4. What I don't know is that 1.2.3.4 is an anycast address.
So my client sends a SYN packet to 1.2.3.4:443 to open the connection. The packet is routed to data center #1. The data center duly replies with a SYN/ACK packet, which my client answers with an ACK packet.
However, due to some bad luck, the ACK packet is routed to data center #2 which is also a destination for the anycast address.
Of course, data center #2 doesn't know anything about my connection, so it just drops the ACK or replies with a RST. In the best case, I can eventually resend my ACK and reach the right data center (with multi-second delay), in the worst case, the connection setup will fail.
Why does this not happen on ingress, but is a problem for egress?
Even if the handshake uses SYN cookies and got through on data center #2, what would keep subsequent packets that I send on that connection from being routed to random data centers that don't know anything about the connection?