Problem with behavioral code for SR latch

Yes, you're right. My third example isn't a valid SR latch.

You're also right, that a SR-latch is asynchronous by design. So if you exactly need it's behaviour, you have to use asynchronous code. "Use a synchronous equivalent" is dedicated to those cases, where don't need exactly asnchronous behaviour.

I'm aware of the fact, that asynchronous behaviour is needed in some designs. E.g. to capture a pulse, that is shorter than a system clock period, you can't avoid it. But you can still try to make the remaining part of the logic synchronous, which considerably eases the implementation by the design compiler.