The commonality of Doors leading from one room to another was mostly something put into place for the servants of the house, Allowing them to go form one room to another room more easily when the family was away.
One thing to keep in mind about 'Mega mansions' of the gilded age, is they were far more like a small "Hotel" then what we think of as a house. Guests would often stay for weeks or months at a time. So have Six or ten guest rooms was common. When someone came over to visit, it was unlikely he'd stay for a few hours and then leave: staying as a guest for months wasn't uncommon, because travel took a really long time. Then, if we go far enough into the past, you had the fact that a manor was often an administrative center of your estate as well as a house, thus it needed all the facilities to allow it to function as such: stables to provide transportation, an office, quarters for the middle managers (who were sometimes noblemen themselves!) etc.
Many "Super Mansions" of old were so large because many rich people wanted all the comforts of the world at their finger tips. Sure they had the money to travel, but at the turn of the century it took weeks to go on a world cruise.
And of course there are the parties. Back then if you wanted to make 'Business connections' the only way to do so was to invite over 50 to 100 other rich people and hope to get along with them. For that you needed vast ballrooms, extra kitchen, hotel like houses to hold so many extra guests.
These days we have the internet...
Take a look at this next house home to Andrew Carnegie