You’re basically correct that cells in series add their voltage, while cells in parallel divide the required current between them, so each one delivers less. Some batteries, such as 9V ones, are actually several cells in series.
One other thing to be aware of here (and this is a gross oversimplification, but useful nonetheless), is that what really matters as far as how much life you’ll get out of a battery is defined by the number of amp-hours. For instance, a 1 amp-hour battery can produce a current of one amp for one hour, or 2 amps for half an hour, or half an amp for two hours, etc. It’s really not quite that simple in real life, but this is a useful approximation. So if we increase the number of amp hours available in our consumer device, we can run it for longer without needing a change of batteries!
Larger batteries, such as D cells, obviously have a larger amp-hour capacity than smaller cells, such as AAA’s. So if your device runs for an hour on a two D cells, it might only run for a few moments on two AAAs, even though AAA’s have the same voltage as D cells.
Ok, now let’s consider a device that is designed to run for, say, 8 hours on two D cells. Could we make it run for the same 8 hours with a whole pile of AAA’s in parallel? Sure! But it’d be very inconvenient to have that many batteries to change. There are other issues that arise in the design of electronics that use parallel batteries as well, such as voltage reversal when one or more batteries go dead before some others.
Another fact that comes into play is the physical form factor of the device in question. For instance, surely you could run a palmtop computer for much longer from D cells than AA’s, but AA’s are thin enough to fit in the physical case.
Your question about “why not configure everything for a 9V transistor battery” can be answered by observing that 9V transistor batteries have a very low amp-hour capacity compared to other, physically larger batteries. Generally, increasing the volume of the battery increases it’s amp-hour capacity, although different types of battery technolgies have different energy densities, which one can measure in terms of amp-hours/cm^3.