The DHCP RFC specifically says that DHCP is not intended for use in configuring routers. The reason is that in maintaining and troubleshooting routers, it is important to know its exact configuration rather than leaving that to be automatically done, and also that you do not want your router’s operation to depend upon the working of yet another server.
It may be possible to configure some types of more general-purpose computers or servers to get their addresses from DHCP and to act as routers. Also, there are remote access servers, often which are usually not true routers, which use DHCP to acquire addresses to hand out to their clients.