A key fact is always omitted from these stories.

So far as we know, nowhere in nature does any organism make a membrane de novo. Every membrane in use anywhere came from extending an existing membrane, and maybe splitting it.

So, arguably, the real basic stuff of life is not nucleotides, but the primordial membrane we are still busy extending.

One thing we can be certain about is that the world where life originated was very little like today's. Besides lacking oxygen, whatever got in the water stayed until it degraded or stuck to something else. Today, anything of any value gets eaten in short order.

We can imagine seas teeming with random nucleotides and RNA. A remarkably simple RNA can reproduce others it bumps into. Once any two of them encountered one another, the seas would instantly be filled with (near) copies of whichever was even infinitesimally faster at it. It wouldn't matter if they were unstable, because they would always be making more.

When you have trapped some in a semipermiable membrane, you are most of the way to life as we know it.