I actually think the parsing part is more important for laymen. Like, there may be a total of 10K programmers who are interested in learning compiler theories, but maybe 100 of them are ever going to write the backend -- the rest of them are stuck with either toy languages, or use parsing to help with their job. Parsing is definitely more useful for most of us who are not smart enough :D
Yeah I agree, that seems vey true. Although the average person probably also benefits more from learning about recursive descent and pratt parsing than LL(k) parser generators, automata, and finding first and follow sets :)