I’ve seen lots of pictures of 1910s/1920s touring cars but I don’t know that I’ve seen one in person- maybe that would answer the question. They seem long enough to easily have three rows of seats, but they generally just have the front and rear seats. Why were they so long? The people in the back must have had enough room to sit on the floor and have a picnic or a poker game.
(I do know from my grandmother that her father used a modified touring car as an ambulance in the 1920s and 1930s, but I’m guessing that was the exception and, as mentioned, it was modified.)
Long wheelbases (the distance between the axles) made for a smoother ride on the rough roads of the day and you got a longer car to accommodate the longer wheelbase. Most engines of the time were also inline engines with at least four or sometimes six or eight cylinders in a row. This meant that you needed a longer hood to cover the engine. Finally, style probably paid a big role.
The styling may make them look bigger than they are.
For comparison an Austin 20 has a length of 5100 mm while a Subaru Outback, a modern four door station wagon, is 4800 mm. A difference of a bit over one foot. The Austin is certainly a big car, but maybe not as big as it looks. The wheelbases are very long as well, helped by the front wheels being set a long way forward.
They don’t seem to have much storage area behind the rear seat. So I’m guessing they carried the luggage inside the passenger compartment, behind the driver’s seat?
Perhaps the seats reclined quite a ways? 
Also, ladies’ hats back then would have required a great deal of space.
It was important to some folks to show everyone their wealth and power. The same thing happens today, but they buy impossibly expensive supercars, such as Ferraris, Lamborghinis, and Bugatti Veyrons.
The long hood was for straight eights and other monstrously huge engines. Seriously, some of those engines looked like they were built for tug boats.
And I’ve seen old Buicks with a fold down 3rd seat behind the driver’s seat. Not sure if that is representative of other cars of that era.
Thanks all.
Wiki article on Straight-eight engines:
Early auto bodies were simply copies of horse-drawn carriages.
If you were rich, you flaunted it (at least many did).
Here is Wiki on the “Phaeton” body style, which was the original name for what became “Touring Car” style.
Actually, until the 1930’s, many auto bodies were carriage bodies - wood frames with sheet metal tacked on.
They had a fold-out rack at the rear of the car, above the bumper, that when folded down could have a truck (hence “trunk”) strapped to it.
As far as the interior, there were often jump seats tucked up behind the front seats that could be pulled out and would face the rear seats.
They have to be long. Otherwise you might accidentally breathe the same air as your chauffeur, who, as a working class schlub, was almost subhuman. 
You are thinking if the “Town Car” body style.
Believe it or not, Ford (homely little Ford) actually made a Town Car. It is among the very rarest of body styles for the Model A (1928-1931; 1932 in Brazil).
Unless I’m mistaken, the common storage solution was a steamer trunk strapped to the back of the car. on the outside.
I suspect that this is why we call the storage compartment in the rear of today’s cars the “trunk.”
Maybe someone could explain why those wacky Brits call it the “boot.”
It’s at the other end of the car from the “bonnet”.
(We all know that American cars only went from the “hood” to the “trunks”. The legs of the people pushing go out to the boots.)
The “boot” was the covered area on a stagecoach where passengers’ luggage was stored. See the leather-covered back end of this example.
This one passes through a few steps to get to its modern sense. We start with:
Boot, the (usually leather) garment that cover the foot and lower leg, which gives us:
Boot, a piece of armour which cover the foot or lower leg or both, which gives us:
Boot, protective metal gear attached to stirrups or stirrup harnesses to protect the rider’s foot or lower leg but which was also useful in mounting and demounting, which gives us:
Boot, a metal bracket or (later) step on the outside of a coach, used when getting in and out, which give us:
Boot, a larger platform on the (out)side of a coach or carriage where an attendant would sit, usually facing outwards (i.e. sideways). When the coach stopped the attendant would jump down, open the door and assist his social betters out of the coach. This gives us:
Boot, a platform at the front or back of a coach or carriage where attendants sat or (more usually) luggage was strapped, which when enclosed gives us:
Boot, the compartment at the back of a car where luggage is carried.
Winningest thread topic and username combo ever.
I don’t know why you think that these cars have too much sitting space. I think it’s the contrary : we’ve become accustomed to have a too small sitting space. Sitting in a modern car isn’t easy and straighforward (you don’t sit in the back of a car the way you would, say, sit on your couch). You have to bend your legs, possibly push away the front seat, you can’t move naturally your legs while sitted nor extend them…The sitting space isn’t spacious at all. It’s as narrow as it can be without sitting becoming plainly uncomfortable.
I find pretty normal that people back them wanted a sitting space where they would feel at ease.
I remember these! Checker cabs in New York used to have them; we loved pulling them down to sit on them when we were little (even if there was plenty of room on the regular seat).