There are of course a variety of good reasons why exponential cost reduction won't continue, such as the cost of raw materials, shipping, and so on - but most importantly that almost nothing works like that for long.
Li-ion battery manufacturing has seen a good uptick in efficiency due to quickly growing demand and a lot of money poured into squeezing out efficiencies, but there is no reason to assume exponential cost reductions to continue indefinitely. Indeed, it does't work that way for nearly any other industrial product, and (current) batteries aren't special in any way that would make them obviously different.
> Similar to what Moore's law did to semiconductors ...
Actually it is not similar at all. Semiconductors were actually special. There was an exponential reduction in feature size for many years, which led to exponential increases in performance, power efficiency, etc, per dollar.
The massive gains were a direct result of the underlying process being scaled in an exponential manner. Almost nothing else works like this, certainly not batteries. The basic chemistry and efficiency of batteries, including Li-on has been pretty much the same for decades. There are occasional improvements in chemistry or anode construction or whatever, but these are a few % here or a few % there, and many claimed improvements don't pan out at all [1]. That's nothing like the doubling of transistor density that continued for decades. In particular, the total storage of batteries is related to number of atoms of the active ingredient, and that generally puts a fairly hard cap on size and other efficiency factors.
Batteries are becoming cheaper because the production has been scaled up and efficiencies of scale achieved, but this will probably follow a similar curve as for any other popular product like lettuce or vehicles. There is no magic [2] and you'll hit a wall pretty quickly.
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[1] Just go back five years and look for "big" battery news, e.g., big suggested improvements in any characteristic and see if any of them are being used today. Very few are.
[2] Of course there might be magic in terms of a very different battery chemistry, or some totally new way of storing energy that replaces batteries. There have been a lot of contenders over the years, but very few winners. A look at the periodic table also indicates that when it comes to batteries you can do better than Li-ion batteries, but not that much better.