[alancalverd]

because you could use any of the above to ensure the current only goes one way through the resistor,

I think you will find that the battery does that.

Indeed, but not necessarily in the direction you want. Why else would anyone put a diode in the circuit? Except possibly a LED or photodiode, but you discounted those in reply #7.

[alancalverd]

The most spectacular form of diode must be the mercury-arc rectifier.

I'm sitting amid a collection of old x-ray components including a thermionic vacuum diode that can handle 1 amp at 150 kV and a Nevitron mercury vapor triode (forerunner of the thyristor) from a unit that I decommissioned in 1990. The anode heat sink of the latter beast still has traces of bird sh1t from the pigeons that had nested in the 3-phase switching cabinet.

As you say, neither of these would be much impressed by a 12V battery, but either would be represented by a generic diode symbol in an introductory lecture.

[vhfpmr]

it's much better to model it as an exponential

An exponential is a polynomial.

Moderator's Note: A discussion on what is an exponential, and how to calculate it was split off to a separate thread:
https://www.thenakedscientists.com/forum/index.php?topic=81727.msg629459#msg629459