no design _must_ include anything..
the access - distribution - core topology is one that scales very well and therefore is often suggested. However, to make an example we have Dreamhack (LAN-party with 5000 attendants) which this year goes from a access-distribution-core network to a access-core network. It is based around two Extreme Networks black diamonds.
Enough with that.
Most oftenly you don't have full mesh between core and distribution unless you only have 2 core routers or at least quite few. If you have say 10 core router, you most oftenly just connect you distribution switch/router to two of the core routers for redundancy.
Why should you change any metric!?!
I'd say it's better to have equal metrics so that you can load balance.
