The fewer external points of access there are on a network, the easier it is to secure the network against external attack. Each connection, which should require a properly configured firewall, introduces one more door that a malicious hacker could break down, so to speak.
As far as security risks, I can only think of one: the introduction of more consolidated single points of failure. That is, if one connection fails, a larger portion of the government will be affected by the outage. However, this availability concern is easily overshadowed by the security improvements gained by reducing the complexity of the network.
Still, through the judicious use of connection sharing and VPN links between sites, it's possible -- and recommended -- for enterprises to consolidate external network connections to a manageable number.
This was first published in February 2009