I'd say it's about intent. Depending on the context, "x * 4" is less clear than the bitshift (For example, when packing multiple values into an integer)
The point isn't "always do multiplication" but to do what makes logical sense. Don't pick your operators for performance, pick them for readability. The compiler will handle the performance aspect for you.
I recommend Matt Godbolt's Talk(s) about compiler cleverness: https://www.youtube.com/watch?v=bSkpMdDe4g4 (see the 30 minute mark for the multiplication example)