Why are non precision approaches not lined up?

Greg Farris wrote:

OK - the VOR is not exactly on the runway centerline - maybe two runway
widths off. Is that the reason then? Are we sure, or just guessing?
Is it better to break out with two runway widths of sidestep, or with the MAP
"on" the extended centerline, but the runway visible out the side window?

My question is why it's done that way. If we're sure that the answer is "to
place the MAP on the centerline, regardless of heading" then that answers my
question.

You're arguing with the criteria. The criteria requires that the final approach
course intercept the runway centerline, extended, at 3,000 feet from the approach
end of the runway. There is a slight parallel option when that is not possible.
If you want to learn all about it, check the TERPs criteria, which is available
on Summit Aviation's Aviation Reference Library CD-ROM.