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