IIR filter concerns in PID control systems
For example if you execute a PID at 0.2Hz then you can control a system with a dynamics max. 0.1Hz according to Shannon. Now if you process 16 taps FIR every 100ms you get a delay of 8 cycles which would be 800ms, which is not so bad, but maybe too much for PID executing every 5000ms. But if you run FIR at 10ms, you get only 80ms delay, or you can run every 1ms and extend to 32,64 taps...
Your theory that you have to process a batch of data doesn't stand, because you have to purge the oldest sample and bring the new sample and compute everything again, each cycle not a record and start all over again.