As someone with a CE/EE degree, I don't really agree.

Like you said, that background does have a lot of benefits. But the downside is that a CE grad typically spends less time doing "software" work than a CS grad. When a CE student is taking courses on circuit design, FPGAs, and CPU architectures, a CS student might be taking courses about databases and concurrency. I don't think I touched SQL or a multithreaded program in a university course. Those were all "high level" things that CS students focused on.

This isn't meant as a knock on CE grads -- I just don't think it's wise to suggest them as the solution to OP's problem since they have their own set of "blind spots" to deal with.