A career in Web Development may be tangled with this feeling of being a mediocre programmer, inferior job, less pay, etc.
BUT (and this is a BIG but) you have to keep in mind that this is just the way you need to start things on the Web. Once you get past the initial growing up period, the realm of Web will then look different and knowledge you swallowed as CS-grad will seem shallow.
There are so many "good" problems that a pompous CS grad might want to handle...
Web is the sexiest place of data -- nobody will disagree that -- lot of companies are dealing in Petabytes of data, and these petabytes are related in myriad of ways with each other. You can start to see how your most deeply learnt techniques/algorithms/design-patterns can look "infant" when it comes to handling this kind of scale.
Read this book to get some taste of web data mining.
SOA, SaaS/PaaS/IaaS, and everybody's favorite -- Cloud Computing -- they all require rigorous applications of CS principles... and Web is the place where these methodologies/patterns are heavily used.
What about "distributed computing" -- must have this as a subject in one of your semesters.
Web is the biggest and most exiting distributed system on the planet -- and no other will ever surpass it in that.
Now, granted, Web pros don't get good $$$ to begin with -- but that's just the nature of it -- there are so many people -- that know web things -- that the common chores just can't earn you big money.
BUT (again a VERY BIG BUT), there is the other side to look at. Web is the cheapest place to innovate -- if you got something good cooking in your mind, all you need is a computer and a decent Internet connection to materialize it.
So I think, web indeed manifests the idea that just getting a CS degree is (and should) NOT be a sure way to earn good bucks -- you've got to have the beautiful mind to come up with something creative (and useful), then the courage to take that something and transform it to something "real", then the perseverance to hold it out when time and people become trying, and most importantly the belief that what you're trying to do -- trying to bring to life -- is worth every bit of your time and effort and will not just succeed but will be a deeply snuggled emotion.