The STS roll control program controlled attitude in response to sensed velocity, rather than attempting to control the trajectory directly. This portion of the flight wouldn't be particularly latency-sensitive.
Spacecraft Guidance, Navigation, and Control Requirements for an Intelligent
Plug-n-Play Avionics (PAPA) Architecture :
In the first stage after lift-off, the objective of the guidance algorithm is
to take the vehicle through the atmosphere while minimizing the fuel spent and keeping the structural loads in their
design range. To achieve that, the algorithm provides attitude commands as a function of the vehicle velocity. These
values are pre-computed and stored in the computer memory.
After the roll program completes, the shuttle does go into closed-loop control to minimize aerodynamic loads, but the overall trajectory guidance remains open-loop until relatively late in the ascent.
Space Shuttle Digital Flight Control System
Five seconds after lift-off, commands
are issued to accomplish the pitch-over and roll-to-flight-azimuth maneuvers.
During regions of high dynamic pressure, a load relief system in both pitch
and yaw minimizes air loads on the vehicle... The load relief function is accomplished
by lateral and normal accelerometer feedbacks blended into the attitude command system starting at 25 seconds into the flight.
During all flight phases, the fundamental flight control computational
cycle is 40 milliseconds. A number of flight control computations take
place only every 80 milliseconds, and some take place approximately once per
second. In addition to the basic 40-millisecond minor cycle requirement,
the total delay between sampling of the flight control sensors and transmittal of the resulting command to the effectors is constrained to be no
greater than 20 milliseconds.
If I'm parsing this correctly, it means that every 40ms, there's a sensor-computer-effector cycle that takes no more than 20ms. The shuttle was notoriously aerodynamically unstable, far more so than most launchers, so I imagine that this sort of cycle time would suffice for almost all.