I don't think a uni degree in web design or related subjects will be enough to start a career in web design. It won't hurt either, of course. But as you said, it won't be up to date and it won't cover really practical stuff. However, learning theoretical approaches to problems in general (with a bias towards web stuff) will be helpful in general. And the earned degree will communicate that you have a certain knowledge and educational level.
But to start a real live career you will need to learn skills. And read about current developments, follow blogs, forums, etc. But the most important thing for being an allround web designer is to learn not only about the technical and visual aspects of creating websites, but also about marketing, SEO, business aspects, and last but certainly not least: copy writing. These things you read about you'll need to practice in real live. Just start creating sites, even it's for family, relations, friends, charity. Don't make them just for yourself, becasue then you won't have a proper client experience, which is essential in your learning path. You'll find that working with actual clients can be very frustrating at times, and also very rewarding. It will push your skills in unexpected directions, and teach you how to deal with "real", professional level clients later on.
I have a masters degree in linguistics and mass communication (1993), and after working for several employers in editorial functions, I started my web design company in 2004, without professional skills. I created simple sites for myself (affiliate stuff) and relations. For peanuts or free, just to build a portfolio and learn real live skills. Until 2006 I did't make anough money to live from, but luckily I had some savings to live from. From 2004 I do earn enough to live from, and it increased every year. My skills and knowledge in ALL aspects of web design are pretty pro level now, although I learn new stuff almost daily. That's what so cool about this line of business.
Altough I do pretty well, I enrolled in an online web design course a few weeks ago, because I felt that web design is more and more about aiming for commercial goals, and less about creating pretty looking sites only. The commercial aspects tend to become the most important aspect clients are looking for. And of course they must be. Having a website as some kind of online brochure is not enough anymore. I feel that my knowledge of creating sites that strive for maximizing conversion is not enough, compared to my technical and visual skills. The course I'm taking now teaches me a lot of things I already know and practice (it is aimed at dedicated beginners), but has a heavy focus on conversion and commercial aspects, and actually it's opening my eyes all the time. It's a very modern course, using many videos and online seminars, along with written stuff and other sources. I'm not sure if I am allowed to tell the name of the course, as the forum rules seem to forbid that. But Google for "online web design course" and you'll probably find it. As it's a very practical, up-to-date course, it may be a good addition to the uni course you're taking. Well, enough about this.
I'm sure there are also other ways to get up-to-date practical pro level skills, so I hope you succeed in finding something you like. There are of course also tons of free materials out there on the web for you to use! Your uni degree will provide ease of mind for clients or employers that are looking for formal education backgrounds, and your practical hands-on skills and knowledge will cater for those who are looking for real world experience and portfolios.