Theoretically, if you consider the departure airport as part of the "route", then 91.181(b) says you should intercept the course.
However, I have not met a single controller who actually expects that. They are expecting you to take off in whatever direction, climb to at least 400 feet (assuming no ODP), and then make a turn direct to the first fix on the route.
I think it's the controller not liking aircraft to be making unexpected 30º turns, and is just as simple as that.
One of the few times I've ever had to exercise captain authority in terms of shutting down my FO was in this sort of scenario, only it was even worse to me: First fix on route was "XYZ", ATC had us on a departure vector, ATC asked us what our course to XYZ was, and then said "resume own navigation". FO wanted to go back to the course from the airport to XYZ even though the controller asked what our course to XYZ was, so he'd obviously (to me, anyway) be expecting us to turn to the course we just gave him. But, FO was a VERY experienced instructor, with more than double (closer to triple!) my total logged time just in dual given, so he was used to the "book" answer, when the real world answer is different.
This is one of those things that really drives me nuts about the FAA - There's often a reg or AIM procedure that made sense back in the VOR days that just doesn't make sense today, and nobody does it any more, but their docs still say that it's how you're supposed to do things. They need an overhaul. It's been nearly 30 years.