In addition to what others have said about route stability, there is possibly a more relevant point to make: for 'ingress' traffic, the anycast IP is the destin

In addition to what others have said about route stability, there is possibly a more relevant point to make: for 'ingress' traffic, the anycast IP is the destination, and for 'egress' traffic it is the source. This distinction is important because the system doesn't have any reasonable way to anticipate where the reply traffic to the anycast IP will actually route to. A packet is launched to the Internet from an anycast IP, and the replies could come to anywhere that IP is announced - most likely not the same place the connection originated. Contrast to when the (unicast) client makes the first move, and the anycast node that gets the initial packets is highly likely to get any follow up packets as well, so in the vast majority of cases, this works just fine.