I don't see that as necessary. For example, life could have started as a tightly bound pattern of molecules on a surface, with RNA as the means to transfer that pattern from one place on the surface to elsewhere. Then RNA could have taken over as the genetic material. It seems implausible to me that RNA be the first genetic material; it's too complicated. I also don't see the necessity to make RNA world protein-free. If RNA took over as genetic material from something else, it might have started as the intermediary between that something else and proteins, just as it is today.
RWP. today is a bad day. I just buried my dog. I am sad.
However, RNA World is not my theory (hypothesis, actually.) Those behind it insist on no proteins -- I think to take into account the unlikely probabilities of proteins forming at random then hooking up with RNA forming at random.
And granted some propose an unknown proto nucleic acid but there is no evidence for it.
And I don't mean to make fun of RNA World because it is actually an interesting and pretty cool attempt to solve abiogenesis.
However, it is far, far, far, far from being ascertained, and considering previous claims that the solution to abiogenesis is just around the corner healthy skepticism is called for -- which, in fairness, many of those investigating it have.
Regardless, God exists and Jesus loves you. Really.