In a vector editor like Illustrator, blend modes do not work in CMYK mode; blend modes only work in RGB mode. My logical conclusion is that you should never use blend modes on a logo design, because you always need a printable version of the logo, and simply copying the logo with blend modes on from an RGB document to CMYK document will mess it up big time; so when you want to "blend" elements, opt for opacity settings instead. And yet a lot of tutorial videos, on YouTube for example, use the blend mode Screen for effects like "glossy buttons" (for example, this one).
I think it's fine to use blend modes on photographs or paintings, because there are too many colors to worry about so you would just want to directly print an RGB document anyway. Logos and identity systems, on the other hand, use very few colors, and the accuracy of printed colors is much more of a concern so you may want to check if your logo looks good in CMYK mode, where blend modes don't work.
So should blend modes ever be used for logo designs?
Never mind. There's nothing wrong with Blend Modes and CMYK Mode. It's just my stupid AMD graphics card failing all this time and I never knew it.