I think it's purely for performance, but it does make a big difference. There's a lot of round trips to set up an SSH connection, and depending on the RTT to the server, that can feel like a real delay if there's another host in the connection. If you use a Proxy host for jumping, and it's got a better RTT to most servers you connect to, reusing the existing connection to it might actually make it feel like it connects faster than a direct connection from your workstation would.
e.g.
$ ping -c 2 foo
PING foo (a.b.c.d) 56(84) bytes of data.
64 bytes from foo (a.b.c.d): icmp_seq=1 ttl=55 time=3.56 ms
64 bytes from foo (a.b.c.d): icmp_seq=2 ttl=55 time=3.62 ms
--- foo ping statistics ---
2 packets transmitted, 2 received, 0% packet loss, time 3ms
rtt min/avg/max/mdev = 3.564/3.594/3.624/0.030 ms
$ time ssh root@foo "echo foo"
foo
real 0m0.650s
user 0m0.062s
sys 0m0.006s
Now if I add the following to .ssh/config:
Host foo
controlmaster auto
controlpath ~/.ssh/ssh-%r@%h:%p
You can see how much faster it gets if I already have a connection to that server open:
$ time ssh root@foo "echo foo"
foo
real 0m0.032s
user 0m0.003s
sys 0m0.004s