Everything would be dead and enshrouded in darkness due to us not being there to hatch the World Destroyer, stop Drakath from getting the World Destroyer for Seppy, or fulfil our part of the prophecy.
Remember that we also played a part in the MS's plan. Without us there to extract the... harder to find orbs, the plan could not have continued. Additionally, the prophecy was made by looking at the future, so realistically, if the Hero never existed the prophecy would be different. If the plan had never gone ahead, Warlic wouldn't have split either, and Jaania wouldn't have founded the Rose...
Basically, either the Hero would have to exist, just not as our player, or the setting is isolated somewhat from previous events. For the purposes of speculation.
Vaal not meeting Roirr means that Vaal and Roirr never go to the future, which means that Secundus never sends them into the past, which means that they never teach Tanislav how to cast Tanislav's Last Will...This ALSO means that Tomix and Vaal are never born
Bear in mind that there had to have been a system of time travel in place to lead up to final time loop. If Roirr died and Tanislav time-traveled, becoming the black robed stranger who sold the younger Tanislav the Will, it could well have led to the final, closed feedback loop.
So if Tomix hadn't released the spirits, something odd would have happened. Since Weaving already existed, it can't have been an original timeline. But Tanislav would have already died by that stage, precluding the possibility of his own time travel. If at any stage in a loop there is no information transfer to a successive timeline... the loop resets, and becomes divergent. Divergent in this usage means it never settles.
(In answer to your actual question)
The Avatar of Time Hero stated that we were among the 'simpler' versions of the potential heroes. Presumably, the methods by which they retain their memories must then be more complex.
If a system is put in place that provides remote relays that can transfer memory between timelines, it would be a simple question of forming a sequence of relays that creates no paradoxes (this can become quite complicated, though still logical; the details are a little convoluted for a post. Also, I'm not entirely clear on how they'd work, exactly...)
One essential feature of this system, though, would be to create a system that enables two paths to the same result; otherwise, there will always be an annoying paradox somewhere.
One example, using books as relays, would be writing something in a book in the first timeline. In the successive timeline, the events are different, so that same book couldn't be written originally. Instead, you copy the text of the book from the previous timeline.
If all that filters through to the final timeline is the text of the book, there is no difference in final result between the different timelines, despite having multiple paths to the same thing. Likewise with memory transfers.
Alternately, the entire issue of changing physicality but not memory is really not a consistent system. You can train in the inn, therefore the regions of your brain that are trained to physical movement are also unaffected. Given this, there is presumably a system in place for wiping the memories of the different versions as they leave. In which case, the founders need simply to make an exception for themselves in this system.
What would have happened had the Hero retained their memories from before the Reset?