Latency, slapback delay and phasing issues from pipe organs in big echoing churches is a subject in its own right.
Here in the UK we still have lots of them in churches, cathedrals and Victorian era concert halls.
I've never played one myself, but according to someone who has latency (in a similar sense to latency in DAWs) can be a real issue with some of them. The complex mechanical couplings and air valves can mean that the organist is actually playing ahead of what is coming out of the pipes. Which besides being tricky in itself means that if the organist makes a horrible mistake they have time to realise exactly what they've done and that there is nothing they can do about it but cringe waiting for the mistake to boom out of the organ.
Incidentally, before pipe organs became the fashionable thing to have church music in England was mostly made by local musicians who'd be located in the church' west gallery. A typical mix might be fiddles, sackbuts, a serpent or two and so on. Whatever instruments the locals could play or owned, and not necessarily in that order.
The novelist Thomas Hardy was a west gallery musician (and a third generation fiddler who also played dance music and left us a very significant manuscript collection of traditional tunes). If he is to be believed west gallery musicians were not always as respectful of their surroundings as they might have been, and had ways of letting the Vicar know if the sermon was boring or the reverend was going on for too long.
Which might in part explain the fashion for the organs which replaced the musicians.