It's only "about" 10 hZ, on that order of magnitude. Indvidually you can have faster components and even though the process is pipelined, the last guidance correction that matters takes the sum total of all component times in the system. The seeker has to see the target is off-axis, then the computer has to calculate the proportional control input, and then the servos actuate the fins.
You also might be overestimating what "current tech" means in military hardware. The PAC-3 Patriots were entered into service from 1995-2000, meaning they were designed with late 1980's technology. The Saudis don't get to have the true top end hardware, the US won't sell their "best stuff" until they have "new best stuff" to beat it.