The “building a website” aspect of CS isn’t something that is well grounded enough to keep its value. CS itself has plenty of value in its entirety; however, in my experience a CS background is better when paired with something more along the lines of “hard engineering disciplines” (“hard” as in opposition to “software” not “easy”). The technologies for web-based work are often too ephemeral to really make a good career. You can make great money now but fail to build useful skills that are going to serve you in the long run if all you do for the next 20 years is learn a new web platform every few years (not to say there isn’t valuable web work, but there absolutely is a lot of junk work there too). While some CS people are able to realize this and find the CS fields that have long-term value, I find that engineering-turned-CS folk do this better.