Default route delete - Core switche

[s.kanth]

We have two router and 2 core switches ,running EIGRP between four devices..

MPLS       DLS link
          \     /
         R     R
          /      \
         /        \
        S--------S

Can we delete  default routes from "ip route 0.0.0.0 0.0.0.0 Next_hop" core switches?

I mean, What will be the significate impact,if those routes deleted from the core switches ?

Thanks

Sri