It's used as a way to identify two things quickly:
Verification of Address
Age of Adopter
Now, if you don't want to provide that, don't make a big deal out of it, but DO ask if there is another way to verify the needed credentials.
I do agree that certain rescue groups have begun making the adoption process a bit of an ego boost. To many hoops to jump through. I've volunteered and run animal rescue for many years, and I've learned that trust, communication and body language go a long way. Plus, if you have a good "take back" policy you're covered.
An adoption contract should really not be more than one page...unless it is a breed specific rescue. Even then, baited questions like, "Will you tether your dog outside" are worthless because even a newbie adopter knows to answer that question with a "No." Open ended questions are better.
Anyway, the point is, that a DL# does have it's worth, but there are plenty of alternatives and a polite refusal works wonders.