Boy, there sure is a lot of confusion out there about "maximum black" and how to achieve it. So let me add to the fray
You can get maximum black (D-max) from any negative with any contrast filter. Just expose long enough. The image may be totally worthless, but you can get as black as you like with enough exposure. Heck, I don't even need a negative or even an enlarger to get paper to D-max; just turn on the room lights and toss it in the developer. D-max is a result of two things: adequate exposure and adequate development - period.
The adage that a fine print must contain a maximum black and a maximum white (just paper-base white) is about as valuable as many other photographic generalizations. Yes, most successful prints have good blacks and good highlights and lots of nicely-separated midtones in between. Some don't and that's just fine too if that's what the goal of the photographer is. I've got a couple of prints with nowhere near D-max in them on purpose. They work well IM-HO.
Besides, achieving a print with a full range of tonalities is really all about the negative that you start with. The idea is to have a negative that has a full range of densities in the right proportions to deliver a fine print when printed on a medium-contrast paper grade or filtration setting. That's why we spend so much time on film exposure and development.
The whole point of exposing a clear area of the negative for enough time to get D-max (or close enough to it to be visually indistinguishable) is to see if you are exposing and developing your
film properly. Making the "proper proof" is a down-and-dirty way of checking to see if your negative has enough exposure and the proper range of densities to get print tonalities that correspond best to the scene (and how the photographer visualized it).
Yes, developing for a too-short time will not allow the paper to reach D-max. This is not good, so develop your prints long enough. Finding how long to develop your prints so they are not underdeveloped is pretty straightforward; read the directions that come with your paper and print developer.
Overdevelopment of prints happens only when fogging starts to occur. That takes a pretty long time with most papers - say 8-10 minutes or longer before any ill effects are noticed. I've developed prints for five minutes and more with no fogging. The upshot here is that the window of development time where you can achieve a maximum black and still have no fogging is really large, somewhere between 1.5 and 6 (or more) minutes for most fiber-base papers.
As mentioned before, extending development time beyond that which is needed for the paper to achieve a maximum black and the characteristic curve shape has stabilized only speeds up the paper. That's just like adding a bit more exposure at the enlarger, nothing more.
So the inevitable conclusions: Expose your paper long enough to get the blacks you want in the print and develop it long enough for those black to appear.
It's good to standardize on a print development time that falls within the window between under- and overdevelopment just so you can make consistent changes in exposure with exposure time at the enlarger. A refinement of that is to use development time to make, in essence, small tweaks of exposure, which might be inconvenient to make with exposure time. This comes when making the final adjustments to a print; not when starting out.
If you print for good, "realistic" midtones and highlights and can't get a decent black, it's not the paper's fault. It's your underexposed and/or underdeveloped negative that is the problem. Similarly, if you need to use extreme contrast settings a lot to get decent prints, you really need to refine your film exposure and development.
Best,
Doremus