If I did an apprenticeship, I feel like my career choices would be limited to that one field that I worked on.
My next job I got hired into a position (although not entry level) that asked for at least 5 years of experience.
Lots of those jobs that "require" experience don't, or you can fudge it by talking about experience you had in college or something. I have no idea why HR departments do that.
They expect people with experience sufficient for the entry-level nature of the position to contact them or include in their cover letter a statement which points out that they lack the arbitrary 5 years but otherwise have X, Y, and Z sufficient to do the job.
For example: most federal agencies required 5 years of experience for legal positions for entry-level legal positions, but frequently hired graduating law students for these same positions (at least until the hiring freezes in 2009 and 2010). To put this in perspective: 5 years is usually the standard experience required for a lawyer to seek certification for a speciality in an area of law...
You cannot learn the skills companies like Siemens are offering like that, definitely not in a way that would get you a job.
Closest to it is how my dad got started, by tinkering with motorcycles in his youth and eventually getting a start in manufacturing, but it was a really really long time before he got a decent job.
I'll disagree when it comes to chemistry and physics. If you are going to be doing either of these in anything above the 200-level classes you are going to need resources you can only get in two places - universities and private/gov't institutions.
Besides that, there is a wealth of knowledge at universities that you can't get from a lot of books. And what if you don't comprehend something? You're paying someone to help you understand.