Of course, you are missing a lot. This is OK as long as you learn.
Here we talk mainly about the primary (non-rechargeable) things.
Why batteries are used traditionally in series: Because of the needed voltages vs what batteries have to offer.
If we skip the "tube" era in electronics, for most purposes one needs few volts to few tens of volts in order to power some transistor-based circuit.
On the other hand, the available electrochemical cells supplied modest voltages, e.g. between 0.5V (Volta pile cell when happy) and 2V (lead-acid battery cell).
Both the cells and the electronic circuits converged somewhat and today a lot of devices operate off a single Li cell (3.0V to 4.2V).
The series connection has its drawbacks - e.g. the unmatched cells (they are always somewhat unmatched) becoming dangerous when overdischarged. For the ordinary zinc-carbon 1.5V cells the danger ends up being electrolyte leaks.
But at least, when left alone, cells connected in series are ok for indefinite period.
What about the parallel connection?
Cells are not made equal even if you want to connect them in parallel. They have subtle (and depending on the quality, not so subtle) voltage differences. If you connect them in parallel, they will try hard to equalize these differences.
The cell with the higher voltage will try to charge the cell with the lower voltage.
But wait, they are not rechargeable! This is why the one with the higher voltage will deplete in these attempts, and the one with the lower voltage will build up gas pressure, heat or just wear off.
This may or may not happen to some visible extent with modern, reputable brand-name, fresh cells. On the other hand, one cannot be sure.
What you will do by paralleling two 9V batteries is actually to combine the drawbacks of both series and parallel connection (they are internally 6 cells of 1.5V).
Even if you manage to get them working right, you won't get much more of energy per volume or mass.
The 9V battery is optimized towards miniaturization. It saves the user from dealing with 6 separate miniature cells and their contacts.
On the other hand, it has additional volume, mass and manufacturing effort spent on the internal connections and the common package. These don't bring you energy, they bring you (supposedly) comfort.
And, the small cells in the 9V battery are worse in energy density in the first place - because of the infamous square/cube effect.
You don't need to believe me. Just get the specifications of these two types and calculate their energy density. For the same chemistry (be it zinc-carbon or alkaline) they differ like 1:2 if you compare 9V to 1.5V AA and maybe 1:3 if you compare to D cells.