Additional insulation does help to some degree. However, heat is like water or electricity and tends to take the path of least resistance. So, say you start with a tank with no insulation (inside or out). The most heat loss will be out the side walls as that has the most surface area. Now say you start insulating those side walls. Now, the largest fraction of heat loss will be out the top/bottom of the tank. Then you start insulating that. Pretty soon, heat carried from the tank up the copper piping and through the water will dominate the losses. The total losses will reduce as insulation is added, but where the majority of the losses occur will shift depending on what paths you close off by adding additional insulation.
So, adding insulation to the side walls will always help to some degree but returns are diminishing. There is a point where there won't be a lot of benefit to adding more insulation to the walls as the majority of the heat loss will start being in other directions/modes. Think of a house. Most of the heat goes out the attic. Although going from R30 to R100 in the attic would help, but the impact may be small if your house is covered with single pane windows and has uninsulated walls. My point is you have to look at the whole system.
If the WH is in a conditioned space, then it doesn't even matter (at least in non-summer months) as the heat loss will go into warming the house. If it is in a garage, be sure to insulate the pipes, etc. while you are at it.
Anyway, that is the take from someone with a couple fancy/expensive degrees.

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