^^^ What Saranac said. Spot on.
From my notes -- The temps of the oil and water phases should be sufficiently warm enough to make the most stable emulsion. Also for stability, the temperature of both phases should be a few degrees of each other when they are emulsified.
The ingredients in the oil phase need to be hot enough to fully melt and sufficiently hot enough to have a low viscosity. Holding the oil phase at temperature is not strictly necessary.
Ingredients in the water phase will become more sanitary during a 20 min hold, but heat-and-hold cannot and was never intended to sterilize. The real point of heating the water phase is not to sanitize -- the heating is needed to bring the water phase to the same temp as the oil phase for best emulsification. If you don't care to gain the sanitizing benefit, you could just heat the water phase to match the temp of the oil phase and proceed to emulsify.
I think the heat-and-hold method as commonly used is an easy to follow procedure for hobby lotion makers. A 20 min hold of the water and oil phases in a hot water bath is going to stabilize the temps of the two phases, ensure all ingredients are well melted and mixed, and give a person the best chance of making a stable emulsion. There's a lot to like with the method, again especially for hobby lotion makers. If one is making lotion on a commercial basis, matters might be different.
According to info about making lotions from Jane Barber, a cosmetic chemist --
"...You DO NOT need to hold the oil phase for 20 mins, however, we will need to heat the oil phase up to the same temperature as the water phase when you combine the phases for a proper emulsion. After the water phase has had 20 minutes at around 75C/165F and the oil phase is also at that temperature; slowly pour one of the phases into the other and mix 3-5 minutes with the stick blender on high...."
And this comment from Bob Zonis, another cosmetic chemist --
"...All other things being equal, a O/W [oil in water] emulsion with smaller oil droplets will be more stable than one with larger droplets.... It is a bit easier to break an oil phase into smaller droplets when the oil/water phases are hot - and the longer you can mix the hot phases together, the better. But - it also costs money to keep a batch hot, so about 30 minutes seemed to be the sweet spot. So, in current circumstances, if you aren't using a polymeric-type emulsifier, heat and hold will always make your emulsion better...."