As of second year, I've now written dozens of mostly trivial school assignments from scratch, and I can't see it being different anywhere else. There is, however, a difference between being able to pump out a command line calendar for processing .ics files or program an alarm clock in assembly, and being able to make something that people would actually want to use from scratch. Having never done the latter, I'm sure I would struggle initially.
I think part of the problem is that CS programs simply aren't structured for large projects. It would be far more realistic to say on day one, "get in groups of three and hand in a functioning program by the end of the term", but that structure just doesn't work for school. Or, if it would, then nobody has the brass to try it.
Wouldn't surprise me. Most of the code written these days is modifications or additions to pre-existing codebases. Projects are usually started from scratch by just one or a few coders, then as it grows a great deal more are hired to specialize in building out certain parts of it - front end, backend, db, etc. The ratio of from-scratch engineers to codebase developers is probably pretty small.
(Joel puts it well in this article: http://www.joelonsoftware.com/items/2005/01/27.html )