Thanks to all who took time to reply and gave valid points as to the questions I posed.
As to "Xtreme": it is what WOODS chose to call this series of mowers. It is like the saying "Extreme Sports" which most don't use any more as a defining term.
In reality it means NOTHING, but it has the
implication of being something extraordinary - which it clearly isn't in this application. It is merely a marketing ploy used to rope in those newbies to mowers, (like me) and those less knowledgeable than those with experience, (you guys :laughing

in all things Bush Hog / Brush Hog, etc.)
The names of Bush Hog and Brush Hog being similar is the same thing as what car manufacturers do, imitation being the sincerest form of flattery.
You don't think it was by accident that Woods coined the term brush hog to compete with Bush Hog do you?!
Take me for instance, if one of you guys told me what I needed to get my field mowed was a Bush Hog and I went looking for one and stumbled across a Brush Hog by Woods I might think it was what you told me to go buy. Another example is Dr. field and brush mowers. Though clearly not the same product by any means the implication is something that one might be led to believe does the same type of work, when clearly they are for and accomplish different tasks.
Extreme or xtreme is like using OFF ROAD for every truck that has 4wd capabilities. In reality it means nothing- except for possibly some minor upgrades, like stiffer shocks or springs. A true off roader would laugh at the need for real heavy duty suspension and other mods before they would use such a truck for off road adventurers.
I fully admit I was fooled by the label on the mower which said Xtreme. I thought by looking at the mower on the dealer's lot that it looked heavy duty enough compared to what I had seen elsewhere at places like TSC, as but one example, and it looked to be strong enough for me regardless of the label pronouncing it's ability to climb tall buildings and cut the biggest bush into *smithereens!
* technical term meaning: obliterate into a bazillion pieces.
In defense of my purchase, not that I need to defend it, BUT, I bought the Woods unit and am Xtremely happy with it so far, partly because my tractor dealer sells them and he is close by if I need anything. And I had been thinking for some time about buying a rear mower anyway, but had not done any real research on them other than looking at various brands at places where they are sold.
I judged the unit I bought based on quality of the appearance, welds, structure, size of bolts, support arms etc., not because it said Xtreme or Kriptonite or anything else.
One remaining question: Why would it be harmful to raise the mower with the shafts installed if the tractor is not running, once the shafts are cut to length? That is the way one is intended to transport the mower is it not?