To broaden Mal's excellent answer, the issue of proper pH is not limited to washed-curd cheeses.
I tend to think in terms of three very broad categories of cheese; I stress this is just my own thinking, and I offer apologies for the massive injustice I am about to do to the incredible diversity of cheeses -- obviously there are all sorts of exceptions to what I am about to propose:
1) Cheeses which need to reach very high / maximum acidity (e.g., pH needs to drop to around 4.5) -- examples include the various bloomy (brie, camembert, etc.) cheeses; some (or all??) blues also fall into this category (I think??), as do the stinky cheeses (again, I think -- I haven't made any stinkies). These cheeses allow the lactic bacteria to go to the limit of what they will do as far as acid production before salt is added; at that point, the salt doesn't restrain the bacteria, but it adds flavor and it plays a part in setting up the cheese for the next stage of ripening. As Mal has described, in the process they loose the calcium phosphate that is necessary for flexible structure; if nothing else acted on them, they would be chalky/crumbly. But the molds/bacterias that then act on these cheeses begin to reverse the pH, bringing it back up, and in the process crossing the point at which the proteins hold onto water. As a result, when they are ripe, they become gooey, even runny.
2) Cheeses which are salted BEFORE pressing -- examples include the various types of cheddar -- these cheeses generally need to reach a certain target pH, usually in the vicinity of 5.2-5.3, before they go into the press. Once the target pH is reached, the cheese is milled (broken/cut into smaller pieces) and salt is added, thus restraining further pH drop. Then the cheese is pressed; since the salt is already added, it doesn't really matter how long it is pressed, so long as excess whey is expelled and a good knit is achieved.
3) Cheeses which are salted AFTER pressing -- examples include the various washed curd cheeses, but also include various thermophilic alpine and Italian cheeses. Once the curds have reached a certain texture/dryness (and maybe also a target pH, but I generally have not been very attentive to that at this stage), the curds are put into the press (possibly initially under whey). They are pressed until the final target pH is reached, usually in the 5.3-5.4 range. Here's the trick: the pressing needs to produce the desired result as far as expelling excess whey and achieving a good knit by the time the target pH is reached. Then the cheese is removed from the press and either brined or dry-salted to constrain further pH drop. The temperature of the cheese during pressing plays a significant factor; ideally, it has cooled to the point that pH drop is very slow by the time the target is reached, giving plenty of time for the salt to work its way inward.
Again, let me stress -- the above is my own compilation/consolidation of what I have read here and in books; I will not be surprised if some or all of it needs correction from others on this forum with greater knowledge! But the bottom line is that, for me, there is really only one target pH to worry about: 5.3-ish. I do check the bloomies that I make to be sure they get on down in the 4-point-somethings, but unlike the other cheeses, I'm not worried about accidentally leaving it too long and letting the pH get too low; I WANT it to get low.
My $0.02 ...
