It is all a matter of what you want your cell or battery for. If you want a large amperage at small voltage, you can have a single cell with large electrde plates, or many cells in parallel. If you want a higher voltage, you need more cells in series. If you want both, then you build a battery of many cells in parallel or large plates, and put many of them in series. Putting many in parallel increases the possible amperage, usually with practical advantages, such as reliability, as compared to using larger plates, but one cannot generalise validly without knowing the appliction. 

There are a lot of pragmatic engineering reasons, but apparently no electrical reasons.

To minimise internal resistance, you want the smallest possible gap between pairs of positive and negative plates, aiming for 2-3 mm. But they must never touch. They are made of lead, a bit like waffles as the lead sulphate is squished into the holes. Batteries get hot, the plates expand and warp, the sulphate oozes out, and so on. So you probably want plates no longer than about 200 mm or they are not rigid enough. That limits the cell width, because you probably want to slide the plates down into support grooves in the cell casing. Plates alternate between positive and negative so that both sides of each plate are next to an opposite polarity plate.

You could make rather long narrow cells, but because of the acid they are normally rubber or plastic, and you have to preserve enough rigidity for handling during manufacturing and maintenance. Also, unless you want some really difficult handling problems in confined spaces, you want to keep the weight of each unit below about 20kg for manual lifting.

You also want a reasonable replacement unit for failures. Typically, some debris or a hot spot shorts two plates together. That ruins the whole cell because all the plates share the same sulphuric acid pool (which becomes depleted and also contaminated by debris), and also share the heat shock and do their own warping. There is also an economic benefit in having a few battery sizes, and bolting them up in serial/parallel arrays, rather than a bespoke maximal cell for each application.

Think about the acid content in a vehicle battery. Under acceleration, braking or cornering, the acid sloshes about. At 1g, it leans at 45 deg. In a big cell, that is a lot of fluid movement, and it could leave some plates high and dry and create hot spots. A small cell traps the acid close to its plates because of the height compared to width.

Small cells limit the potential acid loss in case of damage to a cell. Apart from direct acid burn risk, sulphuric acid liberates chlorine from salt water, for instance. You don't want one crack to liberate gallons of the stuff.

British WWII submarines used lead-acid cells for underwater running, which weighed around 250kg. There would normally be around 48 of them. (This is from memory, from a book about HMS Unbroken when she was damaged in the Meditteranean and 50% of her batteries were breached.) Cells were glass inside a steel protective box, and they were bolted to the keel for ballast and stability. They had a bunch of switchgear so they could be ganged up in different ways for high speed, low speed, recharging and so on. So big cells work, but are best used in a very special application.

I know you can purchase smaller lead cell batteries but why not much larger ones?

What is "much larger"? I know batteries having plates several times

larger in area than a car battery. You find such cells in stationary use

in telefonecentrals or for traction in fork lift machines.

One reason against the biggest plates not mentioned yet

is, that if You have the biggest plates, You will use only one face

ofthe two plates making such a big area cell.

Georg

Telephone exchanges have used lead acid cells since before telephones were invented, well almost. Some batteries for telecomm's use are truely huge and they have very long lives. Take a look at this:

http://www.telephonecollecting.org/battery.htm

Generally, the larger you make the cells the greater the capacity and the lower the internal resistance. Having thin plates and/or plates with small gaps between them may sound nice but cells like this have problems with debris getting stuck between plates.

The larger the battery, the more expensive individual cells are and so we build the battery out of individual cells so that a failed cell can be replaced. Take a look at o9ff the shelf batteries that are available from various manufacturers and you will see that you cna buy them in various capacities and configurations.

Car batteries are a compromise because they are required to work in a hostile environment with little or no care and must be cheap.

Jogged my memory nicely, Stewart.

I remembered a UK utility company whose UPS (uninterruptible power supply) for the 5 mainframes and about 50 workstations, is effectively two rooms full of 500 lead-acid truck batteries, and three fairground generator sets parked under the trees.

Also remembered some 1930's car owner guides collected by my father, who was a motor engineer in the 1950s. Some models of car had a lead battery mounted on the left-hand running board (a kind of step under the doors, built into the back end of the front mudguard). The battery box was even designed as an additional step in some models. Some of these guides gave detailed instructions for maintaining the battery. These were wooden boxes with a lead lining, and the plates were examined, cleaned, and fitted by hand by the owner. You bought your own sulphuric acid from a chemist and diluted it with distilled water, finding the specific gravity with a little floaty gauge called a hydrometer.

One instruction I remember is to add the acid to the water. If you add the water to the acid, the first drop is turned to steam by the energy of solution, and blows a splash of acid into your eyes.

The danger from cars then was obviously not limited to the driving bit.

The big Exide battery you refer to gives 6655 AH (amp-hours) at 2 volts for 1500 kilograms, so it stores around 9 watt-hours per kilo. My Volvo battery stores 70 AH at 12 volts and weights around 15kg, so it stores around 56 watt-hours per kilo. So a modern battery has around six times the energy density of the Exide one. The basic chemistry is the same, so I would assume the design and use of materials is just that much more effective.