I don't think I could attempt frequent heavy benching without a Sling Shot, but with it I believe it to be personally viable.
Thats more or less what I was getting at. High frequency is fine for pressing as long as the load on the shoulders is reduced. The deepest/bottom position is usually the hardest on the shoulders so a slingshot or any device or lift that reduces the load there 1-2+ days a week will be more of a benefit than a detriment. You'll always fine someone which can handle full rom pressing day in and day out, but that doesn't represent anything close to the whole.
The staggered progression on the presses can also be good, especially for the OHP. The staggard progression will also allow the lifter to push a little heavier -- OHP progression doesn't happen overnight so adding many singles per week will require a little less load on the bar.
Frequency has a knack for that Facz. With high frequency, balance is also key to keep the joints and such feeling better, at least for me... curls reduce/prevent elbow pain with pressing, ab work keeps the lower back feeling good, hamstring work keeps the knees feeling good. Shoulder discomfort is usually kept to a minimum doing a decent amount of rows/chins (obviously) but also some work with a different type of press --- I focus on overhead work and also do a lot of rowing/pull ups, but the shoulders don't feel good unless I do some type of horizontal press (DB). If the focus is on the bench... then some overhead work. This stuff is usually very light and easy to complete within a few minutes. Something like a total of 40-60 reps in under 5 minutes will do well. On a side, I use the time guideline to ensure weight isn't heavy enough to f' with recovery.
With the deads... I'm not a fan of high frequency with those. It is among the hardest lifts to recover from, they can also take away from other lower back lifts (squats). Like Steve, some can not only get away with frequent heavy deads, but will also benefit from them. For us mere mortals, if deads are to be done frequently, lighter speed work should make up the bulk of the pulls, only going pretty heavy once every week/2 weeks.
In regard to general intensities... I believe the more you want to push a higher intensity, the more you will have to rely on a daily max to determine the weight on the bar. If progression is planned, your not going to get away with high intensity every day for very long. Deloads will help lengthen the process but even so... high intensity leaves little room for error. You should have a plan when you have crappy days or building up with lighter, medium, heavier weeks can help as can splitting the week up into HLM/LMH/MLH.