Does a STAR always lead you to your first point on the approach?
Over the years I have come to the conclusion that whenever an aviation related question has either one of the two following words;
always never, then the answer is usually false. It looks like you came to the same conclusion to your own question.
I have found that this isn't always the case.
What happens though when ATC can't give you vectors (radar is down) and the STAR doesn't exactly lead you to your approach?
As long as you are not dealing with a simultaneous two-way radio communications failure then ATC
will tell you what they want you to do. We routinely fly RNAV arrivals that transition to RNP RNAV approaches into airports in mountainous terrain without radar coverage. ATC will issue one jet a holding clearance outside of the protected airspace while another jet is flying the approach.
If the radar is out then you will not likely be placed on such a STAR that takes you to a place where you are unable to transition to an approach. If you do happen to be on such a STAR then you should have an EFC (expect approach clearance) or at least an idea of what the plan is.
Either way, when you get to the clearance limit
something is going to happen as we cannot pull over to the side of the road and stop. If ATC is unable to vector you then they must do something with you; further routing, holding or a new clearance.
Yours is an interesting question. If you are not satisfied with the responces here there is good ATC section here on PPRuNe with lots of great controller experience.
Respectfully,
Northbeach