How often are VPNs used across leased lines?

Teacher explained today that Full Mesh VPN topology comes with an additional cost per connection. I then asked him "Why? Aren't VPNs used as an alternative to buying multiple leased lines?". He then told me that you'd still want to use a VPN across the leased line.

Thinking about it, I understand that this would add extra security, but how often is it really done? Is there any downside to this?