Hardware people need to understand how software is used in their designs and be able to write test code, even if someone else writes the production version.
Software people need to understand the hardware they are writing code for, and know when to point out hardware issues that should be changed.
There's a lot of overlap, and being able to do both is valuable.
Of course, there are many software fields that don't involve much hardware....if that's what you really want, go for it. In most cases, ability is what counts, regardless of your prior education.