to prevent drips, it needs to be something soft so it conforms to surface irregularities: copper, plastic, rubber, etc.

Heck , a piece of your belt will work in a pinch.

The crush washer is often referred to in the parts catalog as a "drain bolt gasket", which is a more accurate description.  The head of the drain bolt and the bottom of the oil pan are not always 100% flat and perfect, which can allow slow leakage.  So in addition to helping hold the bolt in place, the crush washer/gasket also deforms slightly as you tighten it to make a better seal and prevent leaks.

So, no, a regular hard/solid washer (that does not deform to fit the gap) will not be adequate.  You don't necessarily have to use the OEM brand gasket, any aluminum crush washer of the correct size from the parts store should be adequate.  If you are stuck and you can't get a new gasket that fits, it is better to re-use the gasket that fits, rather than just any metal washer.  But keep an eye on it for leaks afterwards and make sure you have the correct gasket the next time; you can often get away with re-using it once, but more than that you are asking for trouble.

Cheers!