I honestly do not expect a designer to write css, primarily because they should focus on aesthetics - not writing efficient css. I as a web developer am well suited to write that css, and can do so quite easily.
If the (print) designer is expecting pixel perfection, but knows nothing about css, and hands me an illustrator file, I'm walking away. You likely have things that are either unimplementable, or overly complicated. Examples would be 'this image should be 3", but you made it 5" on my laptop and 2" on my 4k monitor.'
If a (normally print) designer hands me a figma file but can't pull it off themselves, rock on. They likely have some idea of whats possible and what's dumb to try and do.
But honestly, if you're full time web designer specifically, I expect you to be designing in the browser, with some occasional help.
