Problem 1: I can't get this damn div to float to the right of my content.
Problem 2: My network card firmware stops acknowledging commands from the driver after 3 days of high utiliization.
If you think you would assign the same person to "solve these problems with code", you're being silly. People specialize and gain expertise in their areas. Use the right tool for the job.
Indeed, I did ever worked. Of course you need some breadth of knowledge, but unless the place was absolutely tiny, your low-level developers writing VHDL weren't going to be asked to optimize a SQL query or tweak CSS.
There's more than enough work out there, why must a web dev know or care how to twiddle bits, or vice versa?