The closest thread I've found (which didn't show up in the automated suggestions) was What happens if an AC voltage is applied to a battery?. Unfortunately, I felt like the answers were more aimed at the device and schematic drawing instead of a directed explanation of why AC cannot be used to recharge a DC battery. I have a vague understanding of why AC cannot be used in electronics (something about the cycling between voltages would not fit the either "0" or "1" needs of a dc circuit) and I wouldn't expect you to try to teach me a bunch of theory that would require long study and research on my part to go down that road, but I was hoping for a clear explanation on specifically why AC power doesn't work for just charging a battery. My educated guess is that the cycle from negative to positive voltage would some how cancel out the charge.
To charge a battry, you must essentially force the positive and negative ions each to their electrode. When you apply AC you periodically swap the direction in which you force the ions, hence they shuffle back and forth, achieving nothing (except causing heat, and probably damage to the battery).
If you put a short across the terminals it's the same as applying 0V to the terminals. You'll get a thousand+ amps and melted wires and possibly a fire. Considering that an AC voltage produces zero volts 100 to 120 times per second (50 Hz or 60 Hz) as the waveform passes from positive to negative or vice versa, you surely must be able to start realizing the problem.
It's a lot worse than this because when the waveform is negative it's like having two car batteries connected to each other with the wires crossed (smoking big time).
To charge a battery the charging voltage needs to be higher than the battery terminal voltage. As you have realised, alternating voltage will not only go below the battery terminal voltage but will go inverse polarity too. Putting one or more diodes into the circuit to "rectify" the AC is how we solve the problem. The diode only allows current through in the right direction.
Your vague understanding regarding the "0" or "1" needs of an electronic circuit is, as you say, vague and I would recommend that you don't spread it around.
An AC current keeps reversing direction; it spends half the time flowing one way, then the other half flowing the other way. Another way to look at it is that the positive and negative terminals swap on each half-cycle.
A battery has distinct positive and negative terminals which don't change. Connecting up a charger the wrong way discharges the battery, rather than charging it.
If you were to connect an AC supply to a rechargeable battery, it would be charged up for half the cycle, but then discharged for the other half.
The diode pack in a car alternator stops the reversal of the voltage. A single diode could be used to block the current from flowing the wrong way. But a bridge rectifier made from four diodes can re-direct the flow of current so that the alternator then has positive and negative terminals which always have the correct polarity.
AC is short of "Alternative Current". What does alternative current means? It means that the positive terminal of an AC supply is not positive all the time. Sometimes it becomes negative and sometimes it becomes positive. The negative terminal changes its polarity as well. As a result, We can NOT say that a terminal is positive (or negative) in AC. For more information about AC: https://en.wikipedia.org/wiki/Alternating_current
After understanding what AC is, let's imagine what will happen if you connect a battery with AC supply to charge it:
The supply has two terminals. When the first terminal is positive, the battery will start charging. I thing you agree with me. After some time, the first terminal will not become positive anymore. It will become a negative. Then, The battery will Discharge electricity again because the positive terminal of the battery will be connected to the negative terminal of the supply. After some time, the first terminal will become positive again and the battery will charge electricity and so on ...