You could go a step further and talk about computer algorithms or mathematics in general. The only cost there is a pen and a piece of paper. The only cost there is your own time. Some experiments and analyses cost more than others, it's just the nature of things.
Similarly, if you're trying to get a novel battery chemistry to outperform a Tesla car battery or generate a completely novel solar cell, you're not going to be able to accomplish that as an IC researcher. As you point out, there could easily be interim projects along the way to identify various interesting properties that might be useful to your long term goal which aligns with my original statement. When that's out of scope you partner with institutions with access to those resources whether those are big corporations, research institutes, or particle accelerators.
So, nope, bad example. Taking an existing process and giving it a few tweaks will push it around in parameter space, improving something we care about (number of cycles before 80%, let's say), often at the expense of something else, like you can't apply as many coulombs. Congratulations, you've got a thesis. And there are dozens of basic battery processes.
Research in high energy physics (cold fusion is a sub-category), is difficult to cobble together on small amounts however. That's why you see profs and labs banding together to raise sufficient resources just for a couple of experiments. And unfortunately for LENR, a great deal of money was spent in the 50s to 70s with no appreciable outcomes, therefore the funding bodies have become jaded and cynical about continuing to fund further research. The area will likely see a resurgence once those board members retire and bright-eyed folks revisit the field.