> Actual CS research is largely the same as EE research: very, very heavy on math and very difficult to do without studying a lot.

That is largely true of academic research. A critical difference though is that you don't need big expensive hardware, or the like to follow along with large portions of the cutting edge CS research. There are some exceptions like cutting edge AI training work super expensive equipment or large cloud expenditures, but tons of other cutting edge CS research can run even on a fairly low-end laptop just fine.

It is also true that plenty of software innovation is not even tied to CS style academic research. Experimenting with what sort of perf becomes possible via implementing a new kernel feature, can be very important research but isn't always super closely tied to academic CS research.

Even the more hobbyist level cutting edge research for EE will have more costs, simply because components and PCBs are not exactly free, and you cannot just keep using the same boards for every project for several years like you can with a PC.