So I would like to chime in as I see some good points here and would like to see if I can make some distinctions.
First of all, some common problems with both methods: if you do static holds or partial reps, usually the latter, then you are going to use more weight. This is fine if you have prepared yourself and built up gradually, but if you just throw on 125% of your 1rm and start rolling partial reps off the line, then you are looking to get injured because your joints take time to adapt. Now the same is true for touching the chest, if you are weak at the bottom and try to get around this by slamming the weight toward your chest at mach 1 and then rebound through the sticking point, then you are looking to hurt your shoulders and probably a lot of other things. This is just to say, newbies in the gym can get injured doing just about anything not because of some inherent flaw with the exercises but because they are just stupid and don't understand something they read in a magazine. They here, more "weight is superior" out of context and just load up.
Now for the experience trainee, I think both methods are good and individual results may very with some mix of the two methods. So I wanted to clarify one point, Keith when you say you do static holds and partial reps, these dont need to be 1RM but just more weigh than you can carry through a full range of motion? Now if this is the case Matt, then I dont see a problem because a 1RM is extremely relative to the specifics of the exercise. I mean you dont hear people saying you are "maxing out" on dumbbell flys because you are db bench pressing with 3x your fly weight. partial reps and full ROM reps are different exercises and you should treat percentages of 1RM differently for each.
Keith, another question, I understand the idea of maximum leverage but in the bench press, you have maximum leverage at the very top, so I am not sure of how you are training your point of maximum leverage somewhere in the middle. The worst leverage is in the middle somewhere (depending on the person) and that is where most people have their "sticking point". The advantage to working out naer this position is that upon reversal of the weight, you must produce the most force, so doing so at your weakest point will make that point stronger. I know for me, I probably have to use less weight if I take a bench press to this point, rather than all the way down. Usually partial reps stop well sort of this sticking point and that is what allows more weight, but they do nothing to help your strength in the full ROM. I find doing static holds at this weak point to be a great help as a static hold builds the ability to strain against a weight without movement and during a maximum bench press, you will do exactly this straining near your sticking point.
Now, I can see problems training with full range of motion if you have a big deficit between what you can hold at different points in the bench because some points will not gain any strength as they wait around for the weaker ones to catch up.
So my thoughts are in short, that you should train with both methods based on your needs and be smart about recovery and load as to avoid injury.