Actually Frank, your on the right path but your mostly incorrect in the details.
There are several reasons why DP's or DPU's (Distributive Power, Distributive Power Units depending on the concept being used) are placed in a train.
First, it depends on the railroad. The UP and BNSF are heavy users of the technology, with NS and CSX now ordering units with the equipment and trying to get it to work on some of its more challenging locations.
Depending on the railroad and its goals, its mostly to run longer and heavier freight with less crews (why run two 6500 ton trains when you can run one long 12000 ton train?) Its simple economics. More you move with less, the cheaper it is to accomplish this. Not that this always works when you run into problems, and time lost fixing some problems may negate any cost savings. But that's another topic.
Although some trains may have empties behind the DP's when used in a mid train configuration, that's 99% not the case. You can have loads and empties in between the DP's. Its placement of the loads/empties as well as the type of car (if loaded or empty) is determined by railroad rules (known as "Car Placement and Train Make-Up Restrictions".
A weight profile of such a train may be (X for load, "x for empties):
Eng Eng XXXXXXXXXXXXxxxxxxxxxxxXXXXXXXXX Eng XXXxxxxxxxxxXXXXXXXXXX (EOT)
Also the type of grades being encountered may also restrict how the train is made up. Coming into or out of mountain or heavy grades will usually have the train pick up or drop off power after that segment.
It is also determined by the DP(s) power rating. Too much power can jackknife empties or long cars/short cars under certain conditions. There are all sorts of formula's used to determine proper placement. In any case, It cannot be more than 8500ft from the head consist. Any other remote consists behind that one cannot be more than 6000ft from it. This is due to the data radios being used.
If the train just has a rear DP(s), the length is still 8500ft.
Air is important (obviously) but mid train DP's on long trains are still a pain in the *** as the air has to pump to the rear of the train as well as towards the head end (and the head end is still pumping towards the DP's). This means your air will recharge quicker on the front half but may still take quite a bit of time to fully build behind the mid train units. Weather is also a factor. Colder it is, harder to pump the air.
DP's are also mainly used (especially on manifest trains and autoracks) to help keep train forces in check (drawbar/coupler ratings). Too much tonnage or power can break a knuckle (not horrible) or yank out a drawbar (very bad).
Another point, essentially there are no 6000hp units in opeartion. The use of HPT (horsepower per trailing ton) has also been set aside by a few railroads. HPT is not a true measure of what a locomotive can pull. UP has pioneered the concept of TPA or Tons per Powered Axle. Especially with AC units, horsepower does not directly relate to what a locomotive can pull.
You will not see more than two units on a rear of a DP train online due to power limitations (jack knife). If you see three, its usually due to one breaking down and they just tacked another unit on out of convenience. Per rules, its suppose to be setout at the next facility that can repair that engine.
For example, the SD9043MAC uses a 4300HP engine. The SD70ACe also uses the 4300HP engine. However due to electrical gear and other features, the 9043 is only rated at 116,000lbs of effort where as the 70ACe is at 120,000 (the new SD70ACT4 uses a 4600HP engine but power output is still 120,000).
Same goes with GE - The AC4400 is rated at 4390HP, the ES44AC/ET44AC at 4365HP yet they are rated at 121,000lbs. GE has been able to reduce cylinders, improve the electrical gear and keep the tractive effort the same. The BNSF ES44C4's are 4400HP motors are only rated at 105,000lb effort. The 4400HP engine in the Dash-9 results in 115,000lbs.
So, not all horsepower is created equal. There is a mathematical relationship between the two, but HPT is slowly falling out of favor, but still used.
Now, taking Franks example of 8000 tons and two 6000hp units, it will still work. You won't be doing 70mph but with AC traction, its done everyday. Even with two DC SD70's, its a 1.0HPT train and will take .8% grades at 16mph or so. On level or light grades it will make decent time.
DPU's are unmanned and controlled by the lead locomotive. The engineer can run the train for the remote units to follow throttle and dynamic brake commands at the same time as the lead, or can what is called "fence" the remote units to do something different. This is common in undulating grade where the train may be at different elevations at the same time so using this fence will help reduce in train forces.
Now, often on the east coast and some metro/industrial areas, some locals will have a locomotive on the rear. The locomotive is just along for the ride and not in a DP configuration, its there to avoid having to run around the train if it needs to change direction. Its basically there for convenience. Switching in many highly industrialized areas have very little track capacity to turn locomotive power or run around the train.
Distributive power technology has been around since the 1970's, but only recently refined. SP and Southern Railroad used Locotrol (Harris) with varied levels of success. BN tried it out as well and had all sorts of issues like the rest. It went from dials, to desktop boxes and now is integrated into the locomotive control screens. The original radio and control equipment required extended noses to house it (known as Snoot noses).
A good video on the old/original style equipment can be found on this NS training video: