out of curiosity where in Europe do you live and how many hops does it take for you to get to the battle servers when you perform a trace route.
I also live in Europe (United Kingdom) and personally I do not experience anywhere near 600ms of input latency.
Here's my trace route: (I'm from Denmark by the way)
traceroute to 54.209.64.161 (54.209.64.161), 64 hops max, 52 byte packets
1 192.168.1.1 (192.168.1.1) 2.978 ms 0.891 ms 0.794 ms
2 89.150.184.1 (89.150.184.1) 21.128 ms 24.553 ms 22.362 ms
3 te1-1-0.mr1.fb.dk.ip.fullrate.dk (90.185.4.138) 20.422 ms 19.793 ms 21.837 ms
4 xe-3-0-0-0.boanqp7.dk.ip.tdc.net (195.215.109.229) 20.846 ms
xe-7-3-0-0.boanqp7.dk.ip.tdc.net (188.180.68.81) 20.433 ms
xe-3-0-0-0.boanqp7.dk.ip.tdc.net (195.215.109.229) 20.133 ms
5 as0-0.ashbnqp1.us.ip.tdc.net (83.88.31.141) 135.807 ms 136.418 ms 134.936 ms
6 * * *
7 205.251.245.5 (205.251.245.5) 141.979 ms 184.620 ms 139.315 ms
8 205.251.245.123 (205.251.245.123) 137.551 ms 136.632 ms 137.511 ms
As I said earlier, the latency is around 140 ms. This translates into something different in-game though, as seen from the results.
I am pretty sure if you were to record a movie and do the same analysis you would end up with a similar result.