I agree with your post for the most part. But the last paragraph is it bit off: the process of improving chemistry and formulation of the battery cells is not mostly a random/stochastic process (like biological evolution for example) but a very elaborate process with a lot of theoretical work, computer simulations and thought guiding the choice of what prototype to "cook up next". What I mean is a big well funded lab just trying a high volume of chemistries in a more random fashion would have to be very, very lucky to beat a smaller lab with more limited resources but with more brilliant researchers.
There is science that goes into narrowing down the choices to a select set of materials. I don't think anyone is testing lithium-oatmeal batteries. But once the likely materials are decided on, the ratios and whatnot are a hit and miss thing.
Contrast this with an integrated circuit maker. There are a number of chemistries that go into semi-conductor designs, but at this point, the chemistry is well understood. A transistor is made by interfacing two layers of N semiconductors with a P type in the middle, or vice versa. N semiconductor material is made by mixing (called doping) a tiny bit of material from the next column on the periodic table from Silicon and P material is made by mixing in a tiny bit from the column on the other side. This makes one more likely to give up an electron and another more likely to be looking to accept one.
The amount of impurity mixed in is on the order of parts per thousand down to parts per billion. For some applications a base material other than silicon is used. Germanium is one, and there are some compounds used too. If you are an engineer tasked with making a new semiconductor device, you can look up exactly the right chemistry for the application you have. For example transistors being used for an electronic switching application like in any digital electronics you want the material doped so the device switches over from one mode to the other as quickly as possible (from a 0 to 1 to a computer scientist) within the noise limits of your application (the quicker the transition the more noise can be generated by the switching), but if you want an analog application like an audio amplifier, you want different characteristics to the transistors.
All of these factors are known and there are computer simulations where you can test everything out before you ever etch a chip.
Battery tech is a different ball game. The exact way the ingredients mix is not fully understood. An engineer working on this stuff can eliminate a lot of materials because they are too expensive, too dangerous, too rare, or it's obvious they aren't suitable. For example, using plutonium in a battery would probably be a bad idea, even if the chemistry worked well.
In a similar way with making transistors a tiny change in the chemistry can have a big effect on the eventual product, but it's much harder to predict with batteries than with semiconductors. There are fewer variables you need to weigh in semiconductor design, the list of potential materials used in doping semiconductors is a lot shorter, and we have 50 years experience with all these materials. There are some exotic semiconductor formulations in the labs, and some of them may be approaching battery chemistry complexity, but there isn't a dying need for them so development is at a more laid back pace. Battery chemistry is the huge bottleneck in EV development.
Anyway, yes battery labs aren't completely shooting in the dark, but there is a lot more trial and error involved than most other areas of engineering tech development.