I'll take a start at answering this from my home/hobby perspective; hopefully Sailor or others will chime back in from the professional perspective.
For me the key issue is to have all of the necessary parts of the process come together at the right place at the right time. For example, there will generally be an optimal pH at which you want to drain the whey from the curds - not always the same for every cheese; the pH at draining affects the amount of calcium in the curds, and this in turn affects the structure and texture of the cheese. However, there is also an optimal dryness of the curds, achieved by stirring and heating. So if your culture is acidifying too quickly, you may drop past the target pH before the curds are ready (or, if you drain at the right pH, the curds may still be too moist / undercooked). Conversely, if your culture is acidifying too slowly, you may wind up either over-drying the curds or draining when the pH is too high. Likewise when pressing a cheese that is salted after pressing, you need to stop pressing and start salting at the right pH; if you leave it in the press too long and the pH goes too low, you will get a much more crumbly texture than you were looking for. But you need enough time in the press to work your way up from light weight to final weight; if you press too hard too quickly, you will likely close up the rind before all the whey has drained.
Note that, in my experience - which is
not anywhere close to expertise, but consists of making about 100 aged cheeses - even when I use the same cultures in the same amounts at the same temperatures, I can get different results in the rate of acidification. (And when I say "the same cultures," I don't just mean the same variety; I mean the same package!) I believe that the key difference may be the milk at different times - all I have to work with is store-bought, pasteurized, homogenized, "standardized" milk - but still, cows produce different milk at different times in the season. My suspicion is that different batches of milk have different buffering capacity. In any case, the bottom line is that, even though there is a science to cheese making, it remains an art - even when you know the action of the culture(s) you are using, any batch of cheese needs dynamic adjustment along the way to try to get the variables to line up at the right time. (Caldwell's book,
Mastering Artisan Cheese Making, is helpful in pointing out ways to do this.) If the on-the-fly adjustments are not sufficient, then you may need to find a slower or faster acidifier to use with a particular type of cheese.
Again, let me emphasize that I am responding out of my limited experience as a home/hobby cheese maker. I suspect that someone like Sailor can point to additional factors that may lead to choosing faster or slower acidifiers - for example, I think I remember seeing here on the forum that you get more subtle depth of flavor with slower acidification, but I don't know this from my own experience. Meanwhile, as a home/hobby maker, a factor that comes into play is how long the make is going to take, so that I can get to bed at a decent hour.
