Good assertion but I don't see the question is practical. If one is using the magnetic bead based method, that means there is changes in the liquid phase during the extraction/purification process. Thus, it becomes obvious that beads need to be washed and dried to eliminate the carry forward of the liquid phase. Thus, for now, I haven't heard of any such methods.
I understand that the beads need to be washed. But ethanol might not be the best wash solution. It affects downstream reactions. That is why drying step is needed. Just wondering if any methods use a different wash solution that minimum leftover is not harmful.
If you read the protocol carefully it also says, wash buffer III and elution buffer is the same. Of course it is just a company specific name in the kit. Some call it as elution buffer and some call it wash buffer III.
The III (3) also indicate that it is not normal wash, because majority of kits only have 2 wash steps, which is also logical. So, please read carefully and do not get confused.
MagMax kits work robustly, and there is no need for prolonged bead drying. Automated workflows are available as well- on KingFisher duo or prime instruments, in this case you dont need to worry about timing at all
My understanding about the drying during beads-based purification is drying can remove as much ethanol as possible to avoid its' impact on the followup process. And you can not use just water to wash since that may elude your sample as well. Most of the commercial or online protocols are using Ethanol-based wash buffer, which must have the drying steps to remove residual Ethanol. There is a new company (ACTA Science) who is marketing a ethanol free wash buffer, so you can move on to your next step without waiting to get dry. So it's much easier and reliable since you don't need to worry about under drying (may have too much Ethanol left) or over drying (may lead to low yield, specially for longer DNA/RNA fragments. I tried their NimblePure PCR clean up, which works well in my hands.