Can anyone give me an answer as to whether Sheriff's office can or should impound vehicles when driver has no license? I think they can if they arrest them, but not if they drag them to the SO and tell them to find a ride. Any thoughts?

It's an arrestable office. So, if he's arrested and the PD follows its procedures you can impound it.

Get a driver's license and you won't have a problem!

and cars can be held for no insurance violations, which seem to go hand in hand with no license violations.

In Maricle v. Biggerstaff the United States District Court, Northern Distric (Dallas) held that it was not a violation of 42 USC 1983 for a law enforcement agency to have a policy that vehicles would be towed if the operator failed to establish proof of financial responsibility. The court pointed out that it is unlawful to operate a motor vehicle on a public road in Texas without it. I think the same rationale could apply to no DL (I presume the person doesn't have a DL at all).

Janette A